A PROOF OF THE RIEMANN HYPOTHESIS - Louis de BrangesFausto Intilla
Abstract. A proof of the Riemann hypothesis is obtained for the zeta functions constructed from a discrete vector space of finite dimension over the skew–field of quaternions with rational
numbers as coordinates in hyperbolic analysis on locally compact Abelian groups obtained by completion. Zeta functions are generated by a discrete group of symplectic transformations.
The coefficients of a zeta function are eigenfunctions of Hecke operators defined by the group.
In the nonsingular case the Riemann hypothesis is a consequence of the maximal accretive property of a Radon transformation defined in Fourier analysis. In the singular case the Riemann hypothesis is a consequence of the maximal accretive property of the restriction of the Radon transformation to a subspace defined by parity. The Riemann hypothesis for the Euler zeta function is a corollary.
A PROOF OF THE RIEMANN HYPOTHESIS - Louis de BrangesFausto Intilla
Abstract. A proof of the Riemann hypothesis is obtained for the zeta functions constructed from a discrete vector space of finite dimension over the skew–field of quaternions with rational
numbers as coordinates in hyperbolic analysis on locally compact Abelian groups obtained by completion. Zeta functions are generated by a discrete group of symplectic transformations.
The coefficients of a zeta function are eigenfunctions of Hecke operators defined by the group.
In the nonsingular case the Riemann hypothesis is a consequence of the maximal accretive property of a Radon transformation defined in Fourier analysis. In the singular case the Riemann hypothesis is a consequence of the maximal accretive property of the restriction of the Radon transformation to a subspace defined by parity. The Riemann hypothesis for the Euler zeta function is a corollary.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
3. Argumentačný text
Túto tému som zvolil z toho dôvodu netriviálnych znalostí o danej problematike. Počas štúdia na
fakulte informatiky som sa stal členom ateliéru grafického dizajnu a multimédií kde som sa
konkrétne venoval štúdiu fotografie. Aj to ma viedlo k voľbe tejto témy. Názov práce je spoločným
označením dvojice problémov prebraných v tejto práci.
4. Anotácia
V práci sú načrtnuté dve základné problematiky, ktoré sa týkajú optických vád fotografických
objektívov. V texte sú rozobrané jednotlivé typy vinetácie a taktiež spôsoby eliminácie jej vplyvu.
Druhá časť textu sa venuje sférickému skresleniu, jeho typom a prípadnému využitiu.
5. Vinetácia
Pojmom vinetácia sa označuje vada objektívu, ktorá spôsobuje úbytok osvetlenia a sýtosti farieb v
rohoch či na okrajoch fotografie. Jej vznik je spôsobený fyzikálnymi zákonitosťami lomu svetla a
samotnou mechanikou objektívu. Intenzitu vinetácie ovplyvňuje použité clonové číslo a taktiež rôzna
ohnisková vzdialenosť. Trpí ňou majoritná časť ultra-širokouhlých objektívov (z angličtiny ultra-wide
lens) a spolu s rastúcou ohniskovou vzdialenosťou je menej badateľná. Jav sa často využíva zámerne
pre mierne zvýraznenie obrazu komponovaného na stred fotografie a v dnešnej fotografii sa často
pridáva veľmi jednoducho za pomoci software.
Klasické delenie vinetácie je na mechanickú, optickú a prirodzenú. Špecifickým prípadom je pixelová
vinetácia, ktorá je obmedzená na digitálnu fotografiu, konkrétne digitálneho snímača a naopak pre
analógovú je typická vinetácia fotografického filmu. [1]
Tou najbežnejšou je vinetácia optická - trpia ňou všetky objektívy. Jej príčinou je samotná stavba
objektívu. Ten je tvorený sústavou optických členov na jednej osi s výnimkou tzv. tilt-shift objektívov,
teda objektívov kde je táto os zámerne vychýlená. Lúč svetla, prechádzajúci priamo alebo veľmi
blízko tejto osi nemá takmer žiadne straty na intenzite a práve preto je obraz najjasnejší práve v okolí
stredu fotografie. S nárastom uhla, pod ktorým lúč svetla prechádza vstupnou pupilou dochádza k
poklesu intenzity. Práve preto je obraz najtmavší na okrajoch respektíve rohoch fotografie.
Jednoduchým spôsobom eliminácie optickej vinetácie je použitie vyššieho clonového čísla. Iný spôsob
je korigovať tento efekt za pomoci software. [1]
Optická vinetácia (Nikkor 50mm f/1.8G)
Najčastejšou príčinou vzniku mechanickej vinetácie je použitie nevhodného príslušenstva, ktoré
blokuje prienik lúčov z okraju zorného poľa cez vstupnú pupilu a následný dopad na snímací čip.
Vhodným príkladom je nevhodná slnečná clona pre daný objektív, či dvojica súčasne nasadených
filtrov. Na ultra-širokouhlom objektíve môže objaviť vinetácia už pri jednom filtri. V tom prípade je
nutné využitie tenkej (z anglického slim) verzie filtrov. [2] Tento typ vinetácie nie je možné odstrániť
za pomoci software a preto je nutné jej predchádzať používaním vhodného príslušenstva. [1]
Nasledujúci obrázok demonštruje vplyv slnečnej clony určenej pre tele-objektív nasadenej na
objektív širokouhlý.
6. Mechanická vinetácia (Nikkor 18-55mm f/3.5-5.6 AF-S DX VR)
Prirodzená vinetácia, alebo aj pokles osvetlenia, na rozdiel od predchádzajúcich nemá príčinu v
blokovaní lúčov svetla. Tento jav je prirodzený a je možná jeho aproximácia (cos4) zákonom poklesu
osvetlenia. Tento pokles je teda úmerný štvrtej mocnine kosínusu uhla, pod ktorým svetlo dopadá na
snímací čip. Týmto javom trpí najmä dizajn objektívov používaných v kompaktných digitálnych
fotoaparátoch. Tomuto typu vinetácie nie je možné predísť a je nutné ju tak odstrániť za pomoci
software v PC. [2]
7. Optické distorzie objektívu
Distorzia alebo aj sférické skreslenie je monochromatická vada objektívu. Konkrétne sa jedná o
problém pri prenose kriviek. Štandardne ňou trpia najviac širokouhlé objektívy vďaka ich skladbe zo
šošoviek, ktoré majú silné zakrivenie. S nárastom ohniskovej vzdialenosti je výskyt distorzie pomerne
vzácny avšak pri lacnejších objektívoch rozšírený. [3]
V prípade súdkovitého skreslenia (z anglického barrel distortion) sa znižuje zväčšenie pôvodného
obrazu s narastajúcou vzdialenosťou smerom od optickej osi ako je vidieť na obrázku. Vďaka tejto
skutočnosti sa výsledný obraz javí ako natiahnutý na guľu alebo sud. Špeciálnym prípadom v tejto
problematike je objektív rybie oko (z anglického fish-eye lens). Ten je význačný zorným uhlom až
180° a súdkovité skreslenie naopak využíva pre zobrazenie nekonečne širokého poľa do konečného
obrazu. Vďaka tomu vznikajú esteticky zaujímavé a jedinečné fotografie.
Opačným prípadom je poduškovité skreslenie (z anglického pincushion distortion), kde sa s
narastajúcou vzdialenosťou od optickej osi zvyšuje zväčšenie pôvodného obrazu. Ovplyvnené sú línie,
ktoré neprechádzajú optickým stredom, tie sú zakrivené dnu a tým vytvárajú útvar podobný vankúšu
alebo presnejšie ihelničke.
Zaujímavé je využitie tohto skreslenia pri výrobe ďalekohľadov a teleskopov pri elimináciu tzv.
glóbusového efektu (z anglického globe effect). Dôvodom je odstránenie neželanej optickej distorzie
pri tomto type zariadenia.
Špecifickým prípadom je komplexné skreslenie, ktoré vzniká kombináciou súdkovitého a
poduškovitého skreslenia. Od optického stredu sa javí ako súdkovité s plynulým prechodom do
poduškovitého skreslenia smerom ku okrajom poľa. Toto skreslenie je možné vidieť napríklad pri
objektíve s extrémnym rozsahom ohniskovej vzdialenosti, napríklad Nikkor 18-200mm VR. [4]
Zľava súdkovité skreslenie, referenčný snímok, poduškovité skreslenie.
8. Bibliografia
[1] Sidney F. Ray, Applied photographic optics. 3. vyd. Focal Press, 680s. 2002. ISBN 978-0240515403.
[2] Paul Van Walree, Van Walree’s webpage on vignetting Dostupný
z URL: http://toothwalker.org/optics/vignetting.html, 2011.
[3] Roman Pihan, Mistrovství práce s DSLR. 5. vyd. Praha : IDIF, 288s. 2010. ISBN 8090321089.
[4] Ken Rockwell, Nikon 18-200mm VR, Dostupný z URL:
http://www.kenrockwell.com/nikon/18200/18200-distortion.htm, 2008.
Hodnotenie
[1]
- rozsiahla publikácia
- autor je znalý problematiky do najväčších detailov
- aktuálnosť publikácie
- komplexnosť problematiky
- fyzikálny rozmer preberaných tém
[2]
- dostupný on-line
- kompletné zdôvodnenie problémov
- fyzikálny rozmer preberanej témy
- obsahuje neformálne vysvetlenie
[3]
- český autor
- aktuálne vydanie
- kompletná publikácia vhodná pre každého fotografa
- podrobne rozpracované témy
- obsahuje neformálne vysvetlenie
[4]
- dostupný on-line
- uznávaný autor
- dlhoročné skúsenosti autora s testovaním objektívov
- využíva humor
- autor testuje aj mechanické vlastnosti objektívov
