scholarly journals Distribution analogue of the Tumarkin result

2006 ◽  
Vol 133 (31) ◽  
pp. 69-73
Author(s):  
Vesna Manova-Erakovik ◽  
N. Pandeski ◽  
Lj. Nastovski
Keyword(s):  
Rational Functions ◽  
Subject Classification

We give a distribution analogue of the Tumarkin result that concerns approximation of some functions by sequence of rational functions with given poles. AMS Mathematics Subject Classification (2000): 46F20, 30E25, 32A35.

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Global Well-Posedness of the Ocean Primitive Equations with Nonlinear Thermodynamics

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Boussinesq Equations ◽  
Climate Science ◽  
Rational Functions ◽  
Ocean Dynamics ◽  
Global Ocean ◽  
Primitive Equations ◽  
Well Posedness ◽  
Nonlinear Thermodynamics

AbstractWe consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the “primitive equations”, coupled to advection–diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space $${{\mathcal {H}}^{1}}$$ H 1 . The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245–267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739–2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science.

scholarly journals Multiclass emotion prediction using heart rate and virtual reality stimuli

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Aaron Frederick Bulagang ◽  
James Mountstephens ◽  
Jason Teo
Keyword(s):  
Heart Rate ◽  
Virtual Reality ◽  
Nearest Neighbor ◽  
Subject Classification ◽  
Support Vector ◽  
Display Device ◽  
K Nearest Neighbor ◽  
Potential Applications ◽  
Health Rehabilitation ◽  
Emotion Model

Abstract Background Emotion prediction is a method that recognizes the human emotion derived from the subject’s psychological data. The problem in question is the limited use of heart rate (HR) as the prediction feature through the use of common classifiers such as Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Random Forest (RF) in emotion prediction. This paper aims to investigate whether HR signals can be utilized to classify four-class emotions using the emotion model from Russell’s in a virtual reality (VR) environment using machine learning. Method An experiment was conducted using the Empatica E4 wristband to acquire the participant’s HR, a VR headset as the display device for participants to view the 360° emotional videos, and the Empatica E4 real-time application was used during the experiment to extract and process the participant's recorded heart rate. Findings For intra-subject classification, all three classifiers SVM, KNN, and RF achieved 100% as the highest accuracy while inter-subject classification achieved 46.7% for SVM, 42.9% for KNN and 43.3% for RF. Conclusion The results demonstrate the potential of SVM, KNN and RF classifiers to classify HR as a feature to be used in emotion prediction in four distinct emotion classes in a virtual reality environment. The potential applications include interactive gaming, affective entertainment, and VR health rehabilitation.

scholarly journals Metabolic connectivity-based single subject classification by multi-regional linear approximation in the rat

NeuroImage ◽  
2021 ◽  
Vol 235 ◽  
pp. 118007
Author(s):  
Maximilian Grosch ◽  
Leonie Beyer ◽  
Magdalena Lindner ◽  
Lena Kaiser ◽  
Seyed-Ahmad Ahmadi ◽  
...  
Keyword(s):  
Linear Approximation ◽  
Subject Classification ◽  
Single Subject ◽  
Metabolic Connectivity
Sign in / Sign up

Export Citation Format

Share Document