Numerical Treatments of Functional Fredholm Integral Equation in 2D with Discontinuous Kernels

This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.

Engrafted newborn neurons could functionally integrate into the host neuronal network

The limited capability to regenerate new neurons following injuries of the central neural system(CNS)still remains a major challenge for basic and clinical neuroscience.Neural stem cells(NSCs)could nearly have the potential to differentiate into all kinds of neural cells in vitro.Previous studies verified that exogenous transplanted NSCs are capable of

THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

In this paper,we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element,we obtain the condition that the integral is independent of path. At last,we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.

Some Refinement of Holder’s and Its Reverse Inequality

Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.

A SHARP FUNCTION ESTIMATE FOR MULTILINEAR SINGULAR INTEGRAL OPERATORS

A variant shar p function estimate is established for the multilinear singular integral operators. Two applications of this estimate are also given.

Erratum to “The Riemann Hypothesis-Millennium Prize Problem” [Advances in Pure Mathematics 6 (2016) 915-920]

The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part.

α-times Integrated Cosine Operator Functions with Growth ω

For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.

Clean Production and Ecological Industry:A Key to Eco-city Development

Eco-city development is a healthy process towards sustainable development, within the carrying capacity of local ecosystem through changing production mode, consumption behavior and decision instrument based on ecological economics and system engineering. The key to its planning is an ecological integration to make trade-off between economic wealth and environmental health, between material and spiritual civilization, between natural and human eco-cybernetics. Integration, demonstration, citizens’ participation and scientists’ and technician’s catalyzing are the key instruments for the implementation of the ecocity plan. "Clean production" and "ecological industry" are key elements in comprehensive development towards an eco-city. Beyond the technical and management questions, how to interlink production, consumption and reduction at the local and regional level, the spatial and urban dimension should be considered in order to perform an integrative urban eco-space.

ON THE BEST APPROXIMATION MATRIX PROBLEM FOR INTEGRABLE MATRIX FUNCTIONS

In this paper positive definite matrix functionals defined on a set of square integrable matrix valued func- tions are introduced and studied. The best approximation problem is solved in terms of matrix Fourier series. Riemann-Lebesgue matrix property and a Bessel-Parseval matrix inequality are given.

On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag-Leffler Function in the Kernel

In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.

The Riemann Hypothesis-Millennium Prize Problem

This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice of a special type of modified zeta functions allows estimating the Riemann’s zeta function and solving Riemann Problem-Millennium Prize Problem.

ON THE INTEGRABILITY OFRADIAL BASIS FUNCTIONS

In this paper we investigate the integrability of certain radial basis functions.Fromthe following forms of funtion ,where A≥0 and g° we construct the function where J is a finite index set, We show that if is continuous at the origin, then is integrable in Rd.

A Model of Fuzzy Normal Distribution

Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, this paper combines the fuzzy number, like “may-occur”, “very-likely-occur”, “rarely-occur”, to optimize the normal distribution probability density function, to provide a significant method in statistics.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

Hans A.Panofsky’s Integral Similarity Function—At Fifty

Fifty years ago, Hans A. Panofsky published a paper entitled Determination of stress from wind and temperature measurements. In his famous paper, he presented a new profile function for the mean horizontal wind speed under the condition of diabatic stratification that includes his integral similarity function. With his integral similarity function, he opened the door for Monin-Obukhov scaling in a wide range of micrometeorological and microclimatological applications. In a historic survey ranging from the sixties of the past century down to the present days, we present integral similarity functions for momentum, sensible heat, and water vapor for both unstable and stable stratification, where on the one hand free convection condition and on the other hand strongly stable stratification are addressed.

Thinking and Strategy on the Diagnosis and Treatment of Functional Gastrointestinal Disorders with Integrative Medicine

The functional gastrointestinal disorders (FGIDs) are a group of diseases mainly manifested as gastrointestinal functional disorders,including 45 kinds of different diseases,such as functional dyspepsia(FD), irritable bowel syndrome (IBS),functional

Monitoring concept for structural integration of PZT-fiber arrays in metal sheets:a numerical and experimental study

The technique joining by forming allows the structural integration of piezoceramic fibers into locally microstructured metal sheets without any elastic interlayers.A high-volume production of the joining partners causes in statistical deviations from the nominal dimensions.A numerical simulation on geometric process sensitivity shows that the deviations have a high significant influence on the resulting fiber stresses after the joining by forming operation and demonstrate the necessity of a monitoring concept.On this basis,the electromechanical behavior of piezoceramic array transducers is investigated experimentally before,during and after the joining process.The piezoceramic array transducer consists of an arrangement of five electrical interconnected piezoceramic fibers.The findings show that the impedance spectrum depends on the fiber stresses and can be used for in-process monitoring during the joining process.Based on the impedance values the preload state of the interconnected piezoceramic fibers can be specifically controlled and a fiber overload.

Collocation Methods for A Class of Volterra Integral Functional Equations with Multiple Proportional Delays

In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.