This document summarizes research into non-supersymmetric heterotic string vacua that resemble the MSSM. The researchers sought models with 4D N=1 supersymmetry that break to N=0, containing the standard model gauge group and 3 generations of quarks and leptons. They presented an explicit tachyon-free model constructed from fermionic strings using a set of boundary condition basis vectors and GGSO phases. This model separates the observable and hidden sectors but contains a mismatch between fermion and boson numbers requiring future work to cancel the vacuum energy.
In this paper we introduce the concept of connectedness in fuzzy rough topological spaces.
We also investigate some properties of connectedness in fuzzy rough topological spaces.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Tim Maudlin: New Foundations for Physical GeometryArun Gupta
New Foundations for Physical Geometry
Original URL: http://www.unil.ch/webdav/site/philo/shared/summer_school_2013/NYU.ppt
Tim Maudlin
NYU
Physics & Philosophy of Time
July 25, 2013
Unit 1: Topological spaces (its definition and definition of open sets)nasserfuzt
Learning Objectives:
1. To understand the definition of topology with examples
2. To know the intersection and union of topologies
3. To understand the comparison of topologies
In this paper we introduce the concept of connectedness in fuzzy rough topological spaces.
We also investigate some properties of connectedness in fuzzy rough topological spaces.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Tim Maudlin: New Foundations for Physical GeometryArun Gupta
New Foundations for Physical Geometry
Original URL: http://www.unil.ch/webdav/site/philo/shared/summer_school_2013/NYU.ppt
Tim Maudlin
NYU
Physics & Philosophy of Time
July 25, 2013
Unit 1: Topological spaces (its definition and definition of open sets)nasserfuzt
Learning Objectives:
1. To understand the definition of topology with examples
2. To know the intersection and union of topologies
3. To understand the comparison of topologies
In general topology many strong and weak forms of open and closed sets have been defined
and studied. Govindappa Navalagi introduced the concept of semi α-open sets which is a weaker form of
α-open sets. Semi*α-open set is defined analogously by replacing the closure operator by the
generalized closure operator due to Dunham in the definition of semi α-open sets. In this paper we
introduce a new class of sets, namely semi*α-closed sets, as the complement of semi*α-open sets. We
find characterizations of semi*α-closed sets. We also define the semi*α-closure of a subset. Further we
investigate fundamental properties of the semi*α-closure. We define the semi*α-derived set of a subset
and study its properties.
In this slide fourier series of Engineering Mathematics has been described. one Example is also added for you. Hope this will help you understand fourier series.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
I made this presentation for my own college assignment and i had referred contents from websites and other presentations and made it presentable and reasonable hope you will like it!!!
Totally R*-Continuous and Totally R*-Irresolute Functionsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
fourier series of sines and cosines , fourier series for even and odd functions, fourier series for sawtooth wave, fourier series for rectified sine wave and fourier series for arbitrary constants.
Weakly proregular sequence and Cech, local cohomologyryoya9826
Seminar Talk in 慶應数理オンラインセミナー (Keio MathSci Online Seminar) at Online
In this lecture, we introduce weakly proregular sequence by Schenzel, it is introduced to study whether there is an isomorphism between Čech cohomology and local cohomology. In [Sch03], he proved that for the Local cohomology and the Čech cohomology defined by the sequence
a
––
=
a
1
,
…
,
a
r
, there is an isomorphism between these cohomologies if and only if
a
––
is weakly proregular. We give an elementary proof of his theorem without using notions of derived category theory. This seminar is based on preprint (arXiv:2105.07652).
このセミナーでは,[Sch03] による弱副正則列 (weakly proregular
sequence) を紹介する.これは Noether 環において局所コホモロジーと Čech
コホモロジーの間に同型が存在するという定理を非 Noether 環に拡張するた
めに導入されたもので,Schenzel はこれらのコホモロジーを定義する点列
푎1, . . . , 푎푟 が弱副正則列であるとき,かつそのときに限り,これらのコホモ
ロジーの間に関手的な同型が存在することを証明した.この観点において,
上に述べた Noether 環における事実は Noether 環の任意の点列は弱副正則で
ある,という形で理解できる.Schenzel は導来圏の言葉を用いて証明を行っ
たが,本セミナーでは講演者のプレプリント [And21](arXiv:2105.07652) に
基づいて,Abel 圏の言葉のみを用いて説明する.
In general topology many strong and weak forms of open and closed sets have been defined
and studied. Govindappa Navalagi introduced the concept of semi α-open sets which is a weaker form of
α-open sets. Semi*α-open set is defined analogously by replacing the closure operator by the
generalized closure operator due to Dunham in the definition of semi α-open sets. In this paper we
introduce a new class of sets, namely semi*α-closed sets, as the complement of semi*α-open sets. We
find characterizations of semi*α-closed sets. We also define the semi*α-closure of a subset. Further we
investigate fundamental properties of the semi*α-closure. We define the semi*α-derived set of a subset
and study its properties.
In this slide fourier series of Engineering Mathematics has been described. one Example is also added for you. Hope this will help you understand fourier series.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
I made this presentation for my own college assignment and i had referred contents from websites and other presentations and made it presentable and reasonable hope you will like it!!!
Totally R*-Continuous and Totally R*-Irresolute Functionsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
fourier series of sines and cosines , fourier series for even and odd functions, fourier series for sawtooth wave, fourier series for rectified sine wave and fourier series for arbitrary constants.
Weakly proregular sequence and Cech, local cohomologyryoya9826
Seminar Talk in 慶應数理オンラインセミナー (Keio MathSci Online Seminar) at Online
In this lecture, we introduce weakly proregular sequence by Schenzel, it is introduced to study whether there is an isomorphism between Čech cohomology and local cohomology. In [Sch03], he proved that for the Local cohomology and the Čech cohomology defined by the sequence
a
––
=
a
1
,
…
,
a
r
, there is an isomorphism between these cohomologies if and only if
a
––
is weakly proregular. We give an elementary proof of his theorem without using notions of derived category theory. This seminar is based on preprint (arXiv:2105.07652).
このセミナーでは,[Sch03] による弱副正則列 (weakly proregular
sequence) を紹介する.これは Noether 環において局所コホモロジーと Čech
コホモロジーの間に同型が存在するという定理を非 Noether 環に拡張するた
めに導入されたもので,Schenzel はこれらのコホモロジーを定義する点列
푎1, . . . , 푎푟 が弱副正則列であるとき,かつそのときに限り,これらのコホモ
ロジーの間に関手的な同型が存在することを証明した.この観点において,
上に述べた Noether 環における事実は Noether 環の任意の点列は弱副正則で
ある,という形で理解できる.Schenzel は導来圏の言葉を用いて証明を行っ
たが,本セミナーでは講演者のプレプリント [And21](arXiv:2105.07652) に
基づいて,Abel 圏の言葉のみを用いて説明する.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Fuzzy random variables and Kolomogrov’s important resultsinventionjournals
:In this paper an attempt is made to transform Kolomogrov Maximal inequality, Koronecker Lemma, Loeve’s Lemma and Kolomogrov’s strong law of large numbers for independent, identically distributive fuzzy Random variables. The applications of this results is extensive and could produce intensive insights on Fuzzy Random variables
Presentation of the scientific research 2002 2007Amro Elfeki
This presentation summaries the scientific research work performed in the period 2002 to 2007. The research covers several aspects of groundwater flow and transport under uncertainty in heterogeneous geological media using stochastic methods. The presentation summarizes research papers published in this field by the author and his research team.
A complete list of Uq(sl2)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl2)-module algebra structures are discussed.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
m - projective curvature tensor on a Lorentzian para – Sasakian manifoldsIOSR Journals
In this paper we studied m-projectively flat, m-projectively conservative, 𝜑-m-projectively flat LP-Sasakian manifold. It has also been proved that quasi m- projectively flat LP-Sasakian manifold is locally isometric to the unit sphere 𝑆𝑛(1) if and only if 𝑀𝑛 is m-projectively flat.
The First Order Stark Effect In Hydrogen For $n=3$
JM ASHFAQUE
1. Non-Tachyonic Semi-Realistic
Non-Supersymmetric Heterotic String Vacua
Johar Muhammad Ashfaque
University of Liverpool
based on 1506.03114
in collaboration with
P. Athanasopoulos, A. E. Faraggi, and H. Sonmez
Johar Muhammad Ashfaque String Phenomenology
2. Motivation
Seek string models which closely resemble the MSSM with
4D N = 1 theory
Johar Muhammad Ashfaque String Phenomenology
3. Motivation
Seek string models which closely resemble the MSSM with
4D N = 1 theory
with SM gauge group embedding
Johar Muhammad Ashfaque String Phenomenology
4. Motivation
Seek string models which closely resemble the MSSM with
4D N = 1 theory
with SM gauge group embedding
3 chiral generations of quarks and leptons
Johar Muhammad Ashfaque String Phenomenology
5. Motivation
Seek string models which closely resemble the MSSM with
4D N = 1 theory
with SM gauge group embedding
3 chiral generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar Muhammad Ashfaque String Phenomenology
6. Motivation
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1 → N = 0
with SM gauge group embedding
3 chiral generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar Muhammad Ashfaque String Phenomenology
7. Motivation
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1 → N = 0
See also talks by S. Groot Nibbelink, E. Mavroudi
with SM gauge group embedding
3 chiral generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar Muhammad Ashfaque String Phenomenology
8. All roads lead to Rome. (Spanish Proverb)
Conformally Invariant
Johar Muhammad Ashfaque String Phenomenology
9. All roads lead to Rome. (Spanish Proverb)
Conformally Invariant
4D, N = 1 Theory
Johar Muhammad Ashfaque String Phenomenology
10. All roads lead to Rome. (Spanish Proverb)
Conformally Invariant
4D, N = 1 Theory
SM gauge group embedding
Johar Muhammad Ashfaque String Phenomenology
11. All roads lead to Rome. (Spanish Proverb)
Conformally Invariant
4D, N = 1 Theory
SM gauge group embedding
3 generations
Johar Muhammad Ashfaque String Phenomenology
12. All roads lead to Rome. (Spanish Proverb)
Conformally Invariant
4D, N = 1 Theory
SM gauge group embedding
3 generations
ROME: N = 1 → N = 0
Johar Muhammad Ashfaque String Phenomenology
13. The Free Fermionic Construction
A general boundary condition basis vector is of the form
α = ψ1,2
, χi
, yi
, ωi
|yi
, ωi
, ψ
1,...,5
, η1,2,3
, φ
1,...,8
where i = 1, ..., 6
ψ
1,...,5
- SO(10) gauge group
φ
1,...,8
- SO(16) gauge group
Johar Muhammad Ashfaque String Phenomenology
14. The Very Simple Rules
The ABK Rules
[Antoniadis, Bachas, Kounnas, 1987]
One-Loop Phases
C
bi
bj
= ±1 or ±i
Virasoro Level-Matching Condition
M2
L = −1
2 +
α2
L
8 + vL = −1 +
α2
R
8 + vR = M2
R
Johar Muhammad Ashfaque String Phenomenology
15. Non-Supersymmetric Tachyon-Free String Vacua
SO(16) × SO(16)
tachyonic state(s) produced
−−−−−−−−−−−−−−−−→ untwisted sector
[Alvarez-Gaume, Ginsparg, Moore, Vafa, 1986]
The SUSY generator S
Guarantees The Untwisted Tachyon Is Projected OUT.
Johar Muhammad Ashfaque String Phenomenology
16. However...
Problem: There is an abundance of sectors in the 3 generation
semi-realistic models that can potentially give rise to tachyonic
states.
Johar Muhammad Ashfaque String Phenomenology
21. No More SUSY
3 Types of Sectors
Sectors that respect SUSY
Sectors that exhibit SUSY breaking explicitly
For a given sector
ρ ∈ Ξ
SUSY partners would be obtained from
S + ρ
But
(ρ)2
L = 4, (S + ρ)2
L = 8
Sectors with equal number of bosons and equal number of
fermions but with different gauge charges
Johar Muhammad Ashfaque String Phenomenology
22. The Fermi-Bose Degeneracy The Mismatch
nb = nf ⇒ Λ is exponentially suppressed.
Talk by E. Mavroudi
[Abel, Dienes, Mavroudi, 2015]
However, in our non-tachyonic, non-supersymmetric model there is
a mismatch.
Having said that, we believe we can engineer our way to tackle this
problem.
Johar Muhammad Ashfaque String Phenomenology
23. Summary
Generically models without SUSY have tachyons
We found a non-supersymmetric semi-realistic model
Furthermore
This model is tachyon-free (all tachyons are projected out)
Various Types of Sectors
Johar Muhammad Ashfaque String Phenomenology
24. Future Work
Searching For Semi-Realistic Models With Exponentially
Suppressed Cosmological Constant
Cancellation of Non-Vanishing Vacuum Energy Tadpole
Against U(1)A Tadpole
Johar Muhammad Ashfaque String Phenomenology
25. GRACIAS POR TU ATENCI´ON
Johar Muhammad Ashfaque String Phenomenology