Partial Integro Differential Equations (PIDEs) occur naturally in various fields of science and technology. The main purpose of this paper is to study how to solve linear partial integro differential equations with convolution kernel by using the Laplace-Differential Transform Method (LDTM). This method is a simple and reliable technique for solving such equations. The efficiency and reliability of this method is also illustrated with some examples. The result obtained by this method is compared with the result obtained by Double Laplace Transform and Double Elzaki Transform method.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
optimal solution method of integro-differential equaitions under laplace tran...INFOGAIN PUBLICATION
In this paper, Laplace Transform method is developed to solve partial Integro-differential equations. Partial Integro-differential equations (PIDE) occur naturally in various fields of science. Engineering and Social Science. We propose a max general form of linear PIDE with a convolution Kernal. We convert the proposed PIDE to an ordinary differential equation (ODE) using the LT method. We applying inverse LT as exact solution of the problems obtained. It is observed that the LT is a simple and reliable technique for solving such equations. The proposed model illustrated by numerical examples.
Show off the efficiency of dai-liao method in merging technology for monotono...nooriasukmaningtyas
In this article, we give a new modification for the Dai-Liao method to solve
monotonous nonlinear problems. In our modification, we relied on two
important procedures, one of them was the projection method and the second
was the method of damping the quasi-Newton condition. The new approach
of derivation yields two new parameters for the conjugated gradient direction
which, through some conditions, we have demonstrated the sufficient descent
property for them. Under some necessary conditions, the new approach
achieved global convergence property. Numerical results show how efficient
the new approach is when compared with basic similar classic methods.
Exact Solutions of Coupled Parallel Resonant Circuits Equations by Decomposit...AI Publications
In this paper, we provide the solution of a modeled parallel resonant circuit using the decomposition method. The parallel resonant circuit also known as resistor (R) in ohms, inductor (L) in Henry and capacitor (C) in farads (RLC) circuit is used in turning radio or audio receivers. The mathematical models are in a system of ordinary differential equations (ODE), which we solve using the Adomian Decomposition Method (ADM). We discovered that this method gave exact solutions as can be obtained using any traditionally known analytic method. These findings are illustrated in three test problems.
In this paper, we introduced the modified differential transform which is a modified version of a two-dimensional differential transform method. First, the properties of the modified differential transform method (MDTM) are presented. After this, by using the idea modified differential transform method we will find an analytical-numerical solution of linear partial integro-differential equations (PIDE) with convolution kernel which occur naturally in various fields of science and engineering. In some cases, the exact solution may be achieved. The efficiency and reliability of this method are illustrated by some examples.
On solving fuzzy delay differential equationusing bezier curves IJECEIAES
In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
optimal solution method of integro-differential equaitions under laplace tran...INFOGAIN PUBLICATION
In this paper, Laplace Transform method is developed to solve partial Integro-differential equations. Partial Integro-differential equations (PIDE) occur naturally in various fields of science. Engineering and Social Science. We propose a max general form of linear PIDE with a convolution Kernal. We convert the proposed PIDE to an ordinary differential equation (ODE) using the LT method. We applying inverse LT as exact solution of the problems obtained. It is observed that the LT is a simple and reliable technique for solving such equations. The proposed model illustrated by numerical examples.
Show off the efficiency of dai-liao method in merging technology for monotono...nooriasukmaningtyas
In this article, we give a new modification for the Dai-Liao method to solve
monotonous nonlinear problems. In our modification, we relied on two
important procedures, one of them was the projection method and the second
was the method of damping the quasi-Newton condition. The new approach
of derivation yields two new parameters for the conjugated gradient direction
which, through some conditions, we have demonstrated the sufficient descent
property for them. Under some necessary conditions, the new approach
achieved global convergence property. Numerical results show how efficient
the new approach is when compared with basic similar classic methods.
Exact Solutions of Coupled Parallel Resonant Circuits Equations by Decomposit...AI Publications
In this paper, we provide the solution of a modeled parallel resonant circuit using the decomposition method. The parallel resonant circuit also known as resistor (R) in ohms, inductor (L) in Henry and capacitor (C) in farads (RLC) circuit is used in turning radio or audio receivers. The mathematical models are in a system of ordinary differential equations (ODE), which we solve using the Adomian Decomposition Method (ADM). We discovered that this method gave exact solutions as can be obtained using any traditionally known analytic method. These findings are illustrated in three test problems.
In this paper, we introduced the modified differential transform which is a modified version of a two-dimensional differential transform method. First, the properties of the modified differential transform method (MDTM) are presented. After this, by using the idea modified differential transform method we will find an analytical-numerical solution of linear partial integro-differential equations (PIDE) with convolution kernel which occur naturally in various fields of science and engineering. In some cases, the exact solution may be achieved. The efficiency and reliability of this method are illustrated by some examples.
On solving fuzzy delay differential equationusing bezier curves IJECEIAES
In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
In this paper, we make use of the fractional differential operator method to find the modified Riemann-Liouville (R-L) fractional derivatives of some fractional functions include fractional polynomial function, fractional exponential function, fractional sine and cosine functions. The Mittag-Leffler function plays an important role in our article, and the fractional differential operator method can be applied to find the particular solutions of non-homogeneous linear fractional differential equations (FDE) with constant coefficients in a unified way and it is a generalization of the method of finding particular solutions of classical ordinary differential equations. On the other hand, several examples are illustrative for demonstrating the advantage of our approach and we compare our results with the traditional differential calculus cases.
A class of boundary value methods for the complex delay differential equationijscmcj
In this paper, a class of boundary value methods (BVMs) for delay differential equations (DDEs) is considered. The delay dependent stable regions of the extended trapezoidal rules of second kind (ETR2s), which are a class of BVMs, are displayed for the test equation of DDEs. Furthermore, it is showed ETR2s cannot preserve the delay-dependent stability of the complex coefficient test equation considered. Some numerical experiments are given to confirm the theoretical results.
AMS 2000 Mathematics Subject Classification: 65L20, 65M12
Generally it has been noticed that differential equation is solved typically. The Laplace transformation makes it easy to solve. The Laplace transformation is applied in different areas of science, engineering and technology. The Laplace transformation is applicable in so many fields. Laplace transformation is used in solving the time domain function by converting it into frequency domain. Laplace transformation makes it easier to solve the problems in engineering applications and makes differential equations simple to solve. In this paper we will discuss how to follow convolution theorem holds the Commutative property, Associative Property and Distributive Property. Dr. Dinesh Verma"Application of Convolution Theorem" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: http://www.ijtsrd.com/papers/ijtsrd14172.pdf http://www.ijtsrd.com/mathemetics/applied-mathamatics/14172/application-of-convolution-theorem/dr-dinesh-verma
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
In the early twentieth century, major representatives of the Jadid movement became active participants in the socio-political processes in the Turkestan region. Usmonkhoja Polatkhoja, a progressive from Bukhara, was one of the beams not only in the Emirate of Bukhara, but also in Turkestan. He first participated in the reforms and progressives, and later in the national liberation movements, and fought for the prosperity and independence of the country.This article provides information about Usmonkhoja's life and work in Jadidism, revolts, national liberation struggles, and emmigiration.
Flood is one of the natural disaster known to be part of the earth biophysical processes, which its occurrence can be devastating; due to mostly anthropogenic activities and climatological factors. The aim of the research is to identify and map the extent at which the impact of flood due to intense rainfall and rise in water in the study area using geospatial techniques and the specific objectives are to carry out terrain analysis of the study area and to generate flood indicator maps of the study area. The study analyzed rain fall data;, the drainage system and Shuttle Radar Topographic Mission (SRTM 30m) of the area. ArcGIS 10.8 was to modelled and to generate the contributing factors map of the study area. The drainage system was generated through on-screen digitization of topographic map of scale 1:50,000 of Ondo South-West. The mean annual rainfall of Lagos State was generated in the ArcGIS environment from the rainfall data through spatial analysis tool. The SRTM was used in terrain analysis of the study area. The results generated showed the lowest mean annual rain fall of the area 1,700mm and the highest mean annual rain fall was 2,440mm. Digital elevation model (DEM), slope, flow direction were generated from the SRTM. Drainage density of the area was generated using the drainage system. The slope map of the entire area which are classified into five slope classes of very high (14%-48.5%) to high (7.6%-13.9%) to moderately high (4.2%-7.6%) to low (1.5%-4.2%) and very low (0. % - 1.2%).
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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
In this paper, we make use of the fractional differential operator method to find the modified Riemann-Liouville (R-L) fractional derivatives of some fractional functions include fractional polynomial function, fractional exponential function, fractional sine and cosine functions. The Mittag-Leffler function plays an important role in our article, and the fractional differential operator method can be applied to find the particular solutions of non-homogeneous linear fractional differential equations (FDE) with constant coefficients in a unified way and it is a generalization of the method of finding particular solutions of classical ordinary differential equations. On the other hand, several examples are illustrative for demonstrating the advantage of our approach and we compare our results with the traditional differential calculus cases.
A class of boundary value methods for the complex delay differential equationijscmcj
In this paper, a class of boundary value methods (BVMs) for delay differential equations (DDEs) is considered. The delay dependent stable regions of the extended trapezoidal rules of second kind (ETR2s), which are a class of BVMs, are displayed for the test equation of DDEs. Furthermore, it is showed ETR2s cannot preserve the delay-dependent stability of the complex coefficient test equation considered. Some numerical experiments are given to confirm the theoretical results.
AMS 2000 Mathematics Subject Classification: 65L20, 65M12
Generally it has been noticed that differential equation is solved typically. The Laplace transformation makes it easy to solve. The Laplace transformation is applied in different areas of science, engineering and technology. The Laplace transformation is applicable in so many fields. Laplace transformation is used in solving the time domain function by converting it into frequency domain. Laplace transformation makes it easier to solve the problems in engineering applications and makes differential equations simple to solve. In this paper we will discuss how to follow convolution theorem holds the Commutative property, Associative Property and Distributive Property. Dr. Dinesh Verma"Application of Convolution Theorem" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: http://www.ijtsrd.com/papers/ijtsrd14172.pdf http://www.ijtsrd.com/mathemetics/applied-mathamatics/14172/application-of-convolution-theorem/dr-dinesh-verma
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
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In the early twentieth century, major representatives of the Jadid movement became active participants in the socio-political processes in the Turkestan region. Usmonkhoja Polatkhoja, a progressive from Bukhara, was one of the beams not only in the Emirate of Bukhara, but also in Turkestan. He first participated in the reforms and progressives, and later in the national liberation movements, and fought for the prosperity and independence of the country.This article provides information about Usmonkhoja's life and work in Jadidism, revolts, national liberation struggles, and emmigiration.
Flood is one of the natural disaster known to be part of the earth biophysical processes, which its occurrence can be devastating; due to mostly anthropogenic activities and climatological factors. The aim of the research is to identify and map the extent at which the impact of flood due to intense rainfall and rise in water in the study area using geospatial techniques and the specific objectives are to carry out terrain analysis of the study area and to generate flood indicator maps of the study area. The study analyzed rain fall data;, the drainage system and Shuttle Radar Topographic Mission (SRTM 30m) of the area. ArcGIS 10.8 was to modelled and to generate the contributing factors map of the study area. The drainage system was generated through on-screen digitization of topographic map of scale 1:50,000 of Ondo South-West. The mean annual rainfall of Lagos State was generated in the ArcGIS environment from the rainfall data through spatial analysis tool. The SRTM was used in terrain analysis of the study area. The results generated showed the lowest mean annual rain fall of the area 1,700mm and the highest mean annual rain fall was 2,440mm. Digital elevation model (DEM), slope, flow direction were generated from the SRTM. Drainage density of the area was generated using the drainage system. The slope map of the entire area which are classified into five slope classes of very high (14%-48.5%) to high (7.6%-13.9%) to moderately high (4.2%-7.6%) to low (1.5%-4.2%) and very low (0. % - 1.2%).
Work study is a catch-all phrase encompassing a variety of methodologies, including method research and work measurement, that are applied in a variety of contexts and lead to a systematic assessment of all elements that affect the efficiency and economy of the situation under evaluation that is meant to be improved. The main aim of this study is to examine and enhance the process token in manufacturing a Perfume of the famous, well-known, aromatic, and beautiful Taif Roses. Some changes in the process has been suggested using method study and time study method which lead to reduction in process time, labor cost and production cost.
Workers are the maximum precious method of an association. Their importance to institutions requires not most effective the want to draw the trendy bents but additionally the need to preserve them for a long term. This paper specializes in reviewing the findings of former research carried out with the aid of colourful experimenters with the quit to identify determinants factors of hand retention. This exploration almost looked at the subsequent broad factors improvement openings, reimbursement, work- lifestyles balance, operation/ management, work terrain, social aid, autonomy, training and improvement.
Watering plants during the correct time is very important due to scientific reasons. Both underwatering, as well as overwatering, can lead to the growth of unhealthy plants or in extreme cases, the death of the plant/tree. These issues which are the case with most self-gardeners and plant lovers can be solved using the smart irrigation technique. The main purpose of this innovation is to assist plant lovers to continue their passion to grow plants at home with ease. Smart irrigation system helps in monitoring the moisture level which majorly affects plant growth besides other factors such as sunlight, fertility of the soil, etc. The digital planting pot has been designed in a way that it effectively incorporates the idea of smart irrigation. Arduino Uno R3 has been used as the main chip in this project along with a few other components like a soil moisture sensor, relay, and water pump. This project requires coding to synchronize all the components, and function properly. A required test has been carried out to review the functioning of the mechanism. The project was tested by once using the soil with enough moisture in the pot and then the soil with the least moisture. Both times, it worked exactly how it was supposed to function. When the soil with the least moisture was tested, there was a clear indication of a low level of moisture and accordingly, the water pump got triggered to water the plant, and when the soil with enough moisture was tested, there was again the clear indication of the correct level of moisture and the water pump was inactive. All the readings which were displayed on the LCD were checked back and forth during the project. The outcomes were the same as expected. Hence, it shows that every component in this project is actively functioning and the whole project is effectively designed.
Because of its accessibility and flexibility, cloud technology is among the most notable innovations in today's world. Having many service platforms, such as GoogleApps by Google, Amazon, Apple, and so on, is well accepted by large enterprises. Distributed cloud computing is a concept for enabling every-time, convenient, on-demand network access to processing resources including servers, storage devices, networks, and services that may be mutually configured. The major security risks for cloud computing as identified by the Cloud security alliance (CSA) have been examined in this study. Also, methods for resolving issues with cloud computing technology's data security and privacy protection were systematically examined.
This study's goal is to present Solutions for Determining the importance level of criteria in creating cultural resources’ attractiveness from tourists’ evaluation. Data were collected from 558 international tourists who chose Vietnam as the destination for tourism.
The study points out that we need to resolve challenges such as: building a safe, friendly destination, etc., destinations need to review and re-evaluate the services of their products and tourist attractions to prepare for the largest number of visitors and stimulate the domestic tourism market is a good solution: To boost the domestic tourism market, it is necessary to increase domestic flights and train connections to major tourist destinations.
A new convenient and efficient route for the synthesis of two very important hydroxo-bridged stepped-cubane copper complexes viz: [Cu4(bpy)4Cl2(OH)4]Cl2.6H2O (1) and [Cu4(phen)4Cl2(OH)4]Cl2.6H2O (2) have been obtained. This synthetic route from the mononuclear CubpyCl2 complex is easier, more reproducible and afforded the complex in a much higher yield than the other two previously reported procedures which were equally serendipitously discovered. The purity and formation of the complexes were confirmed with elemental (C,H,N) analysis and the details of the UV-Vis, Fourier transform infrared, electrospray ionization mass spectra of both complexes and the single crystal X-ray crystallography of 1 are presented and discussed. X-ray crystallography confirms the absolute structure of the complexes. The complexes were formed via the connection of four copper atoms to four hydroxide bridging ligands and four bipyridyl ligands with two chloride ligands. There are two coordinate environments around two pairs of copper atoms (CuN2ClO2 and CuN2O3) and each copper atom is pentacoordinate with square pyramidal geometry.
Artocarpus heterophyllus Lam., which is commonly known as jackfruit is a tropical fruit, belonging to Moraceae family, native to Western Ghats of India and common in Asia, Africa, and some regions in South America. It is known to be the largest edible fruit in the world. The Jackfruit is an extremely versatile and sweet tasting fruit that possess high nutritional value. Jackfruit is rich in nutrients including carbohydrates, proteins, vitamins, minerals, and phytochemicals. The jackfruit has diverse medicinal uses especially antioxidant, anti-inflammatory, antimicrobial and antiviral properties, anticancer and antifungal activity, anthelminthic activity. Traditionally, this plant is used in the treatment of various diseases especially for treatment against inflammation, malarial fever, diarrhoea, diabetes and tapeworm infection. Jackfruit is a good natural source of phytochemicals such as phenolics, flavonoids and tannins, saponins. The health benefits of jackfruit have been attributed to its wide range of physicochemical applications. The use of jackfruit bulbs and its parts has also been reported since ancient times for their therapeutic qualities. The beneficial physiological effects may also have preventive application in a variety of pathologies.
Myogenic differentiation requires to be exactly explored for the effective treatment of fracture. The speed of healing is affected by skeletal muscle, linked to activation of specific myogenic transcription factors during the repair process. In previous study, we discovered that psoralen enhanced differentiation of osteoblast in primary mouse. In the current study, we show that psoralen stimulates myogenic differentiation through the secretion of factors to hone the quality of repair in fractured mice. 3-month old mice were treated with corn oil or psoralen followed by a tibial fracture surgery. Fractures were tested 7, 14, and 21 days respectively later by histology and images observation. Skeletal muscles including soleus muscle and posterior tibial muscle around the damaged bone were collected for quantitative real-time PCR, HE staining, as well as western blot. Daily treatment with psoralen at seven, fourteen days or twenty-one days improves protein or mRNA levels responsible for the whole myogenic differentiation process, makes the muscle fibers more tightly aligned, and promotes callus formation and development. This data shows that high levels of myogenic transcription factors in the process of fracture healing in mice foster the repair of damaged muscles, and indicates a pharmacological approach that targets myogenic differentiation to improve fracture repair. This also reflects the academic thought of "paying equal attention to both muscles and bones" in the prevention and treatment of fracture healing.
The current pandemic has generated the search for new reliable and economic alternatives for the detection of SARS-CoV-2, which produces the COVID-19 disease, one of the recommendations by the World Health Organization, is the detection of the virus by RT-qPCR methods from upper respiratory tract samples. The discomfort of the pharyngeal nasopharyngeal swab described by patients, the requirement of trained personnel, and the generation of aerosols, are factors that increase the risk of infections in this type of intake. It is known that the main means of transmission of SARS-CoV-2 is through aerosols or small droplets, which is why saliva is important as a relevant means of detecting COVID-19. In this study, a modified method based on SARS-CoV-2 RNA release from saliva is described, avoiding the isolation and purification of the genetic material and its quantification of viral copies; the results are compared with paired pharyngeal/nasopharyngeal swab samples (EF/EN). Results showed good agreement in saliva samples compared to EF/EN samples. On average, a sensitivity for virus detection of 80% was demonstrated in saliva samples competing with EF/EN samples. The use of saliva is a reliable alternative for the detection of SARS-CoV-2 by means of RT-PCR in the first days of infection, having important advantages over the conventional method. Saliva still needs to be studied completely to evaluate the detection capacity of the SARS-CoV-2 nucleic acid, however, the described process is viable, due to the decrease in materials and supplies, process times, the increment in the sampling and improvement of laboratory performance.
A recent study establishes that since 1970, there has been an ecological gap between human needs and the planet's resources, with annual resource demand exceeding the bio-productivity of the planet. Specifically, humanity utilises equivalent of 1.75 earths to produce the ecological resources used, with half of this attributable to food consumption. The present work therefore seeks to provide an empirically-based insight into the environmental sustainability of the EF of food consumption in Ijebu Ode. A descriptive cross-sectional approach was used, and primary data were collected from 400 systemically sampled households via structured questionnaires and analysed descriptively using Microsoft Excel and inferentially using mathematical models for calculating ecological footprints. Findings revealed that the household EF of food consumption in Ijebu Ode is 0.05gha per capita, with the footprint of cereal consumption (0.17gha; 37%) taking the major share, followed by meat with a footprint of 0.11gha (23.9%). As a result, it was concluded that Ijebu Ode has sustainable food consumption, which is necessary for its environmental sustainability. However, the sustenance of the former requires creating awareness of the need for sustainable consumption and prioritisation of integrated and population-wide policies and food intervention initiatives to encourage attitudinal change in favour of sustainable food consumption while fostering sustainable food production strategies amidst current environmental realities.
The symmetry occurs in most of the phenomena explained by physics, for example, a particle has positive or negative charges, and the electric dipoles that have the charge (+q) and (-q) which are at a certain distance (d), north or south magnetic poles and for a magnetic bar or magnetic compass with two poles: North (N) and South (S) poles, spins up or down of the electron at the atom and for the nucleons in the nucleus In this form, the particle should also have mass symmetry. For convenience and due to later explanations, I call this mass symmetry or mass duality as follows: mass and mass cloud. The mass cloud is located in the respective orbitals given by the Schrödinger equation. The orbitals represent the possible locations or places of the particle which are determined probabilistically by the respective Schröndiger equation.
Metal-organic molybdenum complexes were synthesized by the hydrothermal method using ammonium heptamolybdate as the metallic source, and as the organic ligand terephthalic acid (BDC) or bis(2-hydroxyethyl) terephthalate (BHET), obtained via glycolysis of poly(ethylene)terephthalate (PET). The BDC-Mo and BHET-Mo complexes were characterized by XRD, N2 physisorption, TGA, ATR-FTIR, SEM, XPS and their in vitro biocompatibility was tested by porcine fibroblasts viability. The results show that molybdates (MoO4-2) are coordinated to the carbonyl functional groups of BDC and BHET by urea bonding (-NH-CO-NH-) which is related to their high biocompatibility and high thermal stability. These organic molybdate complexes possess rectangular prism particles made up of rods arrays characteristics of molybdenum oxides (MoO3). The organic complexes BDC-Mo and BHET-Mo do not show to be cytotoxic for porcine dermal fibroblasts growing on their surface for up to 48 h of culture.
Exercise training with varying intensity increases maximal oxygen intake (VO2max), a strong predictor of cardiovascular and all-cause mortality. Purpose: The aim of this study was to find out the influence of low intensity aerobic training on the vo2 max in 11 to 14 years school girls in Hyderabad district. Methodology: The research scholar has randomly selected thirty (N=30) high school girls were selected as subjects and their age ranged between 11 to 14 years. The subjects were divided into two equal groups, each group consist of 15 total 30. Group one acted as experimental group (EG) and group two acted as control group (CG). The dependent variable vo2 max was selected and it is measured by manual test. Statistical Tool: The statistical tool paired sample ‘t’ test was used for analysing of the data and the obtained ‘t’ ratio was tested for significance at 0.05 level of confidence. Results: The analysis of the data revealed that there was a significant improvement on vo2 max by the application of low intensity aerobic.
Hybrid rice has the potential to outperform existing inbred rice and was said to have the potential to produce 14-20 % more yield. In response, Malaysia Government has introduced its very own first Hybrid Rice Variety knew as Kadaria 1 developed by MARDI. This is in line with one of the strategies outlined in Dasar Agromakanan Negara (DAN) 2011-2020 as an approach to increasing rice productivity within Malaysia. The next step would be developing our hybrid seed rice production system. Therefore, an experiment to determine the planting ratio and planting distance between 0025A (A)-a hybrid with MR283 (R)-inbreed variety was carried out. Planting ratios studied in this study were 2:4, 2:6, 2:8, and 2:10 while planting distance was 14 x 30 cm, 16 x 30 cm, and 18 x 30 cm. Statistical analyses suggested that yield R, yield A, and panicle number A were significantly affected by planting ratios while yield A was significantly affected by an interaction between planting distance and planting ratios. Panicle number A performed significantly higher at planting ratios of 2:4 compared to 2:10. Yield R shows higher significant performance under ratio 2:6 compared to 2:4 and 2:8. Relatively, yield A performed the best under planting distance of 18 x 30 cm. Furthermore, under this particular planting distance, the planting ratio of 2:10 shows the highest significant figure while 2:8 exhibits statistical parity. Both yield R and yield A were significantly affected by planting ratios and have a significant positive association with each other. Therefore, the planting ratio of 2:10 should be the best since it contributed to significantly highest value for yield A while yield R under 2:10 shows statistical parity with 2:6 which was the highest significant value. In conclusion, the combination of 2:10 with a planting distance of 18 x 30 cm was the best since it shows best potential for both yields A and yield R
Cassava plays an important role in improving food security and reducing poverty in rural areas. Despite its importance, its production in Senegal remains low compared to other African countries. Nowadays, it is confronted with numerous constraints. It is in this context that a study was conducted on the cassava production system in the Thiès "cassava granary" region, with the objective of examining farmers' cultivation practices. It was conducted in eight communes located in the department of Tivaouane, some of which are located in the Niayes agro-ecological zone and others in the central-northern groundnut basin. Surveys were conducted among the largest cassava producers in these communes. Analysis of the results showed that cassava is only grown in the rainy season with the same cultivation practices that have been used for years. Of the five varieties listed by the President of the Senegalese Cassava Interprofession, only four are grown in the areas surveyed. The Terrasse (43%) and Kombo (36%) varieties are grown more by our respondents in the Niayes area. Soya (75%) and Wallet "Parydiey" (20% of our sample) dominate in the central-northern groundnut basin.
Cassava plays an important role in improving food security and reducing poverty in rural areas. Despite its importance, its production in Senegal remains low compared to other African countries. Nowadays, it is confronted with numerous constraints. It is in this context that a study was conducted on the cassava production system in the Thiès "cassava granary" region, with the objective of examining farmers' cultivation practices. It was conducted in eight communes located in the department of Tivaouane, some of which are located in the Niayes agro-ecological zone and others in the central-northern groundnut basin. Surveys were conducted among the largest cassava producers in these communes. Analysis of the results showed that cassava is only grown in the rainy season with the same cultivation practices that have been used for years. Of the five varieties listed by the President of the Senegalese Cassava Interprofession, only four are grown in the areas surveyed. The Terrasse (43%) and Kombo (36%) varieties are grown more by our respondents in the Niayes area. Soya (75%) and Wallet "Parydiey" (20% of our sample) dominate in the central-northern groundnut basin.
We are witnessing very demanding and stressful times in which we live, and an occupation that is particularly exposed to stress and different working conditions is the job of a nurse. Exposing themselves to everyday challenges and stressful situations, nurses reach a stage of great emotional and physical exhaustion, lethargy, dissatisfaction, and poorer work achievements, which we know as burnout. The aim of this paper was to determine whether there is and to what extent professional burnout is present in nurses and technicians working in nursing homes across Slovenia and Croatia. The paper is answering the questions of the extent of the burnout influenced by individual characteristics (age, education, years of service and work experience at the current workplace). The study involved a validated questionnaire “The Oldenburg Burnout Inventory (OLBI)” to measure professional burnout. Surveying of the nurses was conducted online at their home institutions. The results show that all respondents have a medium or high level of professional burnout, while no one has a low level or shows no signs of burnout. In terms of age, the group from 55-65 years of age had the highest relative level of burnout in the age group category. With regard to education, the highest burnout was measured in registered nurses.
Hepatitis B and C are one of the most commonly transmitted viral infections through needlestick injury apart from HIV. It is highly prevalent in India and many other developing countries. It accounts for high mortality rate globally amongst low socio-economic groups of individuals. Healthcare workers, especially dental professionals are at higher risk of infection due to high exposure to saliva, blood and sharps. Accidental occupational exposure to non-sterile conditions and its development to more critical and fatal conditions can be reduced through vaccination, prophylactic medications and practicing high safety measures.
This review article focuses on transmission of hepatitis through sharps injuries in medicine, especially dentistry, its prevention, management, post-exposure prophylaxis and the corresponding content.
More from Associate Professor in VSB Coimbatore (20)
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
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Where, and are constants or the functions of alone and ( ) , ( ) are known functions.
2.2. Laplace Transform
The Laplace transform of a function ( ) is define by,
̅( ) * ( )+ ∫ ( )
Where, is real or complex.
The Laplace transform of first and second order partial derivatives are as follows:
) { } ̅ ( )
) { } ̅ ( )
) { } ̅( ) ( )
) { } ̅( ) ( ) ( )
Using Laplace transform convolution theorem becomes,
{ ̅( ) ̅( )} ( ) ( ) ∫ ( ) ( )
2.3. Double Laplace Transform (DLT) [1]
The Double Laplace transform of a function ( ) in the positive quadrant of the -plane is defined by,
̅( ) * ( )+ ∫ ∫ ( )
Where, are real or complex.
The double Laplace transform of first and second order partial derivatives are as follows:
) { } ̅( ) ̅( )
) { } ̅( ) ̅( )
) { } ̅( ) ̅( ) ̅ ( )
) { } ̅( ) ̅( ) ̅( )
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2.4. Double Elzaki Transform (DET) [2]
The Double Elzaki transform of a function ( ) in the positive quadrant of the -plane is defined by,
( ) * ( )+ ∫ ∫
. /
( )
Where, are real or complex.
The Double Elzaki transform of first and second order partial derivatives are as follows:
) { } ( ) ( )
) { } ( ) ( )
) { } ( ) ( ) ( )
) { } ( ) ( ) ( )
2.5. Differential Transform Method (DTM) [3,4]
Let the function ( ) is arbitrary analytic and continuously differentiable function of defined on , -
and then,
( ) { ( )}
* +
( ) ∑ ( )( )
( ) ∑ ( )
We give the proofs of properties of one dimensional DTM in the following theorem:
Theorem 1: If ( ) is differential transform of ( ) then
) ( ) ( ) ( ) {
) ( ) ( )
) ( ) ( ) ( )
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) ( ) ( ) ( )
) ( ) ( ) ( )( ) ( ) ( )
) ( ) ( ) ( ) ( ) ∑ ( ) ( )
Proof: ) Let, ( )
( ) { }
* ( ) ( ) +
If ( )
If ( )
( ) ( ) {
) The proof is obvious.
) Let, ( )
( ) { }
{ ( )} ( ) ( )
Similarly we can prove ( ).
) Let, ( )
( ) { }
( ) ( ) ( ) ( ) ( ) ( ) ( )
) Let, ( ) ( ) ( )
( ) { ( ) ( )}
{∑ } ( ) ∑ ( ) ( )
We summarize the properties of one dimensional DTM in the following table:
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Table 1. Properties of one dimensional DTM
Original Function ( ) Transformed function ( )
{
{
( )
( )
( ) ( )
( ) ( ) ( ) (
)
( ) ( ) ∑ ( ) ( )
3. Applications to Linear PIDE
3.1. Double Laplace Transform Method
Applying double Laplace transform to ( ),
∑ [ ̅( ) ∑ ( ( ))] ∑ [ ̅( ) ∑ ( ( ))]
̅( ) ∑ ̅( ) [∑ ( ( ))] ̅( )
This is an algebraic equation in ̅( ). After factorizing it and applying inverse DLT, an exact solution of ( )
will be achieved.
3.2. Double Elzaki Transform Method
Applying double Elzaki transform to ( ),
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∑ [ ( ) ∑ ( ( ))] ∑ [ ( ) ∑ ( ( ))]
( ) ∑ ̅( ) [∑ ( ( ))] ( )
This is an algebraic equation in ( ). After factorizing it and applying inverse DET, an exact solution of ( )
will be achieved.
3.3. Laplace Differential Transform Method
Applying Laplace transform w. r. t ( ),
∑ { } ∑ { } * ( )+ ∑ { ( ) } * ( )+
∑ ∑ ( ) ∑ { ( ) } ( ) ( )
Equation ( ) is an ODE. This ODE will be solved by one dimensional differential transform method and then by
inverse LT, an exact solution of linear PIDE will be achieved.
4. Results and Discussion
Example 1: Consider PIDE
∫ ( ) ( ) ( )
With initial conditions ( ) ( ) and boundary condition ( ) .
Double Laplace Transform [1]: Applying DLT, we get
( ) ( )
( )
( )
( )( )
( )
Applying inverse DLT,
( )
Double Elzaki Transform [2]: Applying DET, we get
( ) ( )
( )( )
( )
( )( )
( )
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Applying inverse DET,
( )
Laplace-Differential Transform method:
Applying LT with respect to on (3) and using ( ) ( )
( )
( ) ( ) ( ) ( )
Now applying DTM
̅( )
( )
{( ) ̅( ) ( )} ( )
Now applying the Laplace transform to boundary condition
( ) ̅( )
Put in equation (7),
̅( ) ̅( ) . /
̅( ) . / ̅( ) . /
( ) ∑ ̅( )( ) ( )
Now applying Inverse LT,
( ) (Also shown in graphical presentation: see Fig. 1)
Example 2: Consider PIDE
∫ ( )
( ) ( ) ( )
With initial conditions ( ) ( ) and boundary conditions ( ) ( )
Double Laplace Transform [1]: Applying DLT, we get
( ) ( )
( )
( ) ( )
Applying inverse DLT,
( )
Double Elzaki Transform [2]: Applying DET, we get
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( ) ( ) ( ) ( )
( ) ( )
Applying inverse DET,
( )
Laplace-Differential Transform method:
Applying LT with respect to on (8) and using ( ) ( )
( )
( ) ( )
( )
( )
Applying DTM,
̅( )
( )( )
{( ) ̅( ) ( ) . / ( ) ( )} ( )
Now applying the LT to boundary conditions we get,
( )
( )
̅( ) ̅( )
Put in equation (12),
̅( ) ̅( )
̅( ) ̅( )
( ) ∑ ̅( )( )
Applying inverse LT
( ) (Also shown in graphical presentation: see Fig. 2)
Example 3: Consider PIDE
∫ ( ) ( ) ( )
With ( ) ( ) ( ) ( ) ( ) ( ) .
Double Laplace Transform [1]: Applying DLT, we get
( ) ( )
( )( )
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( )
( )
( )
Applying inverse DLT,
( )
Double Elzaki Transform [2]: Applying DET, we get
( ) ( )
( )( )
( ) ( )
Applying inverse DET,
( )
Laplace-Differential Transform method:
Applying LT with respect to on (7) and using ( ) ( ) ( )
( ) ( )( ) ( ) ( ) ( )
Now applying DTM
̅( )
( )( )( )
*( )̅( ) ( ) ( )+ ( )
Now applying the LT on boundary conditions we get,
( )
( ) ( )
̅( ) ̅( ) ̅( )
Put in equation (17) we get,
̅( ) ̅( )
̅( ) ̅( )
( ) ∑ ̅( )( )
Applying inverse Laplace Transform
( ) (Also shown in graphical presentation: see Fig.3)
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Fig.1. Solution of ( ) Fig.2. Solution of ( ) Fig.3. Solution of ( )
In this section, we have solved linear PIDEs with a convolution kernel of different order by using DLT, DET and
LDTM. The graphical solution also been presented. It is observed that the DLT method reduces the linear PIDE
with convolution kernel into algebraic equations (4), (9), and (14). Similarly, the DET method also reduces linear
PIDEs into algebraic equations (5), (10) and (15). These algebraic equations take a lot of computational effort and
time for their factorization and to achieve an exact solution of the problem. It has also been observed that the same
solutions achieved by using LDTM method too. In the LDTM method, the Laplace transform reduces linear PIDEs
into ordinary differential equations which are solved by the Differential Transform Method then the series solution
of linear PIDEs is obtained by applying the inverse Laplace transform. In some cases, an exact solution can be
achieved.
5. Conclusion
In this paper, the Laplace Differential Transform Method was successfully applied on linear Partial Integro
Differential Equations with a convolution kernel. It is observed that, the solutions obtained by the LDTM method
are the same as the DLT and DET methods. The LDTM gives a series solution and in some cases, the exact solution
can be achieved. We firmly ascertained that LDTM takes less computational effort and time than others. It is
concluded that LDTM is an alternate method to solve such kind of PIDEs. This method is a very simple, powerful
and reliable for solving such problems. We hope some other types of PIDE can be used in various fields of
modeling real life phenomena.
Declarations
Source of Funding
This research did not receive any grant from funding agencies in the public, commercial, or not-for-profit sectors.
Competing Interests Statement
The author declares no competing financial, professional and personal interests.
Consent for publication
Author declares that he/she consented for the publication of this research work.
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References
[1] Ranjit R. Dhunde and G. L. Waghmare, (2015). Solving Partial Integro-Differential Equations Using Double
Laplace Transform Method. American Journal of Computational and Applied Mathematics, 5(1): 7-10.
[2] Mohand M. Abdelrahim Mahgob, (2015). Solution of Partial Integro-Differential Equations by Double Elzaki
Transform Method. Mathematical Theory and Modeling, 5(5): 61-66.
[3] Avinash Khambayat and Narhari Patil, (2014). Differential Transform Method for system of Linear Differential
Equations. Research Journal of Mathematical and Statistical Sciences, 2(3): 4-6.
[4] Suchita Moharir and Narhari Patil, (2012). Applications of Differential Transform Method for Solving
Differential and Integral Equations. Scientific Reviews and Chemical Communication, 2(3): 293-298.
[5] K. Kumari, (2015). Exact Solution of Linear and Nonlinear Klein Gordon Equations Using Laplace Differential
Transform Method. International Journal of Applied Mathematics and Mechanic, 4(1): 33-44.
[6] K. Kumari and P. K. Gupta, (2015). Application of Laplace Differential Transform Method to Solve Nonlinear
PDEs with Boundary Conditions. 3rd International Conference on Innovative Approach in Applied Physical,
Mathematical/Statistical, Chemical Sciences and Emerging Energy Technology for Sustainable Development.
[7] K. Kumari , P. K. Gupta and G. Shanker, (2016). Coupling of Laplace Transform and Differential Transform for
Wave Equations. Physical Science International Journal, 9(4): 1-10.
[8] D. Deborah and A. Moyosola, (2021). Laplace Differential Transform Method for Solving Nonlinear Non
homogeneous Partial Differential Equation. Turkish Journal of Analysis and Number Theory, 8: 91-96.
[9] Yuvraj G. Pardeshi, Vineeta Basotia and Ashwini. P. Kulkarni, (2019). Solution of Partial Integro Differential
Equations using MDTM and Comparison with Two Dimensional DTM., International Journal of Scientific &
Technology Research, 8(11): 1215-1221.
[10] Yuvraj G. Pardeshi, Vineeta Basotia and Ashwini. P. Kulkarni, (2019). Solution of Partial Integro Differential
Equations Using Two Dimensional DTM. International Jour. of Research and Analytical Reviews, 6(2): 112-117.
[11] Yuvraj G. Pardeshi, Vineeta Basotia and Ashwini. P. Kulkarni, (2020). Solving Partial Integro Differential
Equations using Modified Differential Transform Method. Asian Journal of Applied Science and Technology,
4(3): 109-118.