A SIMPLE CONDITION OF FERMAT WILES THEOREM MAINLY LED BY COMBINATORICS

2021 ◽  
Vol 51 (1) ◽  
pp. 55-75
Author(s):  
Junya Sebata
Keyword(s):  
Simple Condition

scholarly journals Predicting the Characteristics of Defect Transitions on Curved Surfaces

Soft Matter ◽  
2021 ◽  
Author(s):  
Siddhansh Agarwal ◽  
Sascha Hilgenfeldt
Keyword(s):  
Critical Size ◽  
Complex Function ◽  
Lattice Defects ◽  
Curved Surfaces ◽  
Simple Condition ◽  
Shape Parameters ◽  
Optimal Position

The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which...

scholarly journals Sound Richness of Music Might Be Mediated by Color Perception: A PET Study

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Masayuki Satoh ◽  
Ken Nagata ◽  
Hidekazu Tomimoto
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Multisensory Integration ◽  
Regional Cerebral Blood Flow ◽  
Traditional Music ◽  
Simple Condition ◽  
Regional Cerebral Blood ◽  
Subtraction Technique ◽  
Posterior Portion

Objects. We investigated the role of the fusiform cortex in music processing with the use of PET, focusing on the perception of sound richness.Method. Musically naïve subjects listened to familiar melodies with three kinds of accompaniments: (i) an accompaniment composed of only three basic chords (chord condition), (ii) a simple accompaniment typically used in traditional music text books in elementary school (simple condition), and (iii) an accompaniment with rich and flowery sounds composed by a professional composer (complex condition). Using a PET subtraction technique, we studied changes in regional cerebral blood flow (rCBF) in simple minus chord, complex minus simple, and complex minus chord conditions.Results. The simple minus chord, complex minus simple, and complex minus chord conditions regularly showed increases in rCBF at the posterior portion of the inferior temporal gyrus, including the LOC and fusiform gyrus.Conclusions. We may conclude that certain association cortices such as the LOC and the fusiform cortex may represent centers of multisensory integration, with foreground and background segregation occurring at the LOC level and the recognition of richness and floweriness of stimuli occurring in the fusiform cortex, both in terms of vision and audition.

scholarly journals MATHEMATICAL MODELLING OF THE REMOVAL OF ORGANIC MICROPOLLUTANTS IN THE ACTIVATED SLUDGE PROCESS: A LINEAR BIODEGRADATION MODEL

2018 ◽  
Vol 60 (2) ◽  
pp. 191-229
Author(s):  
MARK I. NELSON ◽  
RUBAYYI T. ALQAHTANI ◽  
FAISAL I. HAI
Keyword(s):  
Residence Time ◽  
Wastewater Treatment Plants ◽  
Activated Sludge Process ◽  
Simple Condition ◽  
Removal Mechanism ◽  
Organic Micropollutants ◽  
Adsorption Model ◽  
Micropollutant Removal ◽  
Effluent Stream ◽  
Steady State Solutions

Before wastewaters can be released into the environment, they must be treated to reduce the concentration of organic pollutants in the effluent stream. There is a growing concern as to whether wastewater treatment plants are able to effectively reduce the concentration of micropollutants that are also contained in their influent streams. We investigate the removal of micropollutants in treatment plants by analysing a model that includes biodegradation and sorption as the main mechanisms of micropollutant removal. For the latter a linear adsorption model is used in which adsorption only occurs onto particulates.The steady-state solutions of the model are found and their stability is determined as a function of the residence time. In the limit of infinite residence time, we show that the removal of biodegradable micropollutants is independent of the processes of adsorption and desorption. The limiting concentration can be decreased by increasing the concentration of growth-related macropollutants. Although, in principle, it is possible that the concentration of micropollutants is minimized at a finite value of the residence time, this was found not to be the case for the particular biodegradable micropollutants considered.For nonbiodegradable pollutants, we show that their removal is always optimized at a finite value of the residence time. For finite values of the residence time, we obtain a simple condition which identifies whether biodegradation is more or less efficient than adsorption as a removal mechanism. Surprisingly, we find that, for the micropollutants considered, adsorption is always more important than biodegradation, even when the micropollutant is classified as being highly biodegradable with low adsorption.

scholarly journals Tradability and the Labor‐Market Impact of Immigration: Theory and Evidence From the United States

Econometrica ◽  
2020 ◽  
Vol 88 (3) ◽  
pp. 1071-1112 ◽  
Author(s):  
Ariel Burstein ◽  
Gordon Hanson ◽  
Lin Tian ◽  
Jonathan Vogel
Keyword(s):  
United States ◽  
Labor Market ◽  
The United States ◽  
Simple Condition ◽  
Foreign Born ◽  
Real Wages ◽  
Local Labor Market ◽  
Relative Wages ◽  
Theoretical Mechanism ◽  
Using Data

In this paper, we study how occupation (or industry) tradability shapes local labor‐market adjustment to immigration. Theoretically, we derive a simple condition under which the arrival of foreign‐born labor into a region crowds native‐born workers out of (or into) immigrant‐intensive jobs, thus lowering (or raising) relative wages in these occupations, and we explain why this process differs within tradable versus within nontradable activities. Using data for U.S. commuting zones over the period 1980–2012, we find—consistent with our theory—that a local influx of immigrants crowds out employment of native‐born workers in more relative to less immigrant‐intensive nontradable jobs, but has no such effect across tradable occupations. Further analysis of occupation labor payments is consistent with adjustment to immigration within tradables occurring more through changes in output (versus changes in prices) when compared to adjustment within nontradables, thereby confirming our model's theoretical mechanism. We then use the model to explore the quantitative consequences of counterfactual changes in U.S. immigration on real wages at the occupation and region level.

scholarly journals Ample Spectrum Contractions and Related Fixed Point Theorems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1033 ◽  
Author(s):  
Antonio Francisco Roldán López de Roldán López de Hierro ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Point Of View ◽  
Strict Inequality ◽  
Simple Condition ◽  
Auxiliary Functions ◽  
Simulation Functions ◽  
Contractive Maps ◽  
R Functions

Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.

scholarly journals Explicit formulas for local factors in the Euler products for Eisenstein series

1989 ◽  
Vol 113 ◽  
pp. 37-87 ◽  
Author(s):  
Paul Feit
Keyword(s):  
Dirichlet Series ◽  
Rational Function ◽  
Eisenstein Series ◽  
Fourier Coefficients ◽  
Simple Condition ◽  
Explicit Formulas ◽  
Local Factors ◽  
Euler Products ◽  
Infinite Sums

Our objective is to prove that certain Dirichlet series (in our variable q−s), which are defined by infinite sums, can be expressed as a product of an explicit rational function in q−s times an unknown polynomial M in q−s Moreover we show that M(q−s) is 1 if a simple condition is met. The Dirichlet series appear in the Euler products of Fourier coefficients for Eisenstein series. The series discussed below generalize the functions α0(N, q−s) used by Shimura in [12], and the theorem is an extension of Kitaoka’s result [5].

scholarly journals Some New Characterizations andg-Minimality and Stability ofg-Bases in the Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xunxiang Guo
Keyword(s):  
Hilbert Spaces ◽  
Frame Theory ◽  
Schauder Basis ◽  
Simple Condition ◽  
Similar Role ◽  
Perturbation Result

The concept ofg-basis in the Hilbert spaces is introduced by Guo (2012) who generalizes the Schauder basis in the Hilbert spaces.g-basis plays the similar role ing-frame theory to that the Schauder basis plays in frame theory. In this paper, we establish some important properties ofg-bases in the Hilbert spaces. In particular, we obtain a simple condition under which some important properties established in Guo (2012) are still true. With these conditions, we also establish some new interesting properties ofg-bases which are related tog-minimality. Finally, we obtain a perturbation result aboutg-bases.

scholarly journals The Accretion-Powered Jet Propagations and Breakout Criteria for GRB Progenitors

2011 ◽  
Vol 7 (S279) ◽  
pp. 363-364
Author(s):  
Hiroki Nagakura ◽  
Yudai Suwa ◽  
Kunihito Ioka
Keyword(s):  
Conversion Efficiency ◽  
Mass Flux ◽  
Accretion Rate ◽  
Opening Angle ◽  
Relativistic Hydrodynamics ◽  
Simple Condition ◽  
Two Dimensional

AbstractWe investigate the propagation of accretion-powered jets in various types of progenitor candidates of GRBs. We perform two dimensional axisymmetric simulations of relativistic hydrodynamics taking into account both the envelope collapse and the jet propagation. In our simulations, the accretion rate is estimated by the mass flux going through the inner boundary, and the jet is injected with a constant accretion-to-jet conversion efficiency η. By varying the efficiency η and opening angle θop for more than 30 models, we find that the jet can make a relativistic breakout from all types of progenitors for GRBs if a simple condition η ≳ 10−3 (θop/20°)2 is satisfied, that is consistent with analytical estimates, otherwise no explosion or some failed spherical explosions occur.

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