# THE MAPPINGS OF DEGREE 1

## Related Articles

- Equivalence Classes of Linear Mappings on B(M). HEJAZIAN, S.; AGHASIZADEH, T. // Bulletin of the Malaysian Mathematical Sciences Society;2012, Vol. 35 Issue 3, p627
Let M be a Hilbert C+-module over the C+-algebra A , B(M) the C+-algebra of all adjointable operators onM, L(B(M)) the algebra of all linear operators on B(M). For a property P on B(M) and Ã¸1,Ã¸2 Ïµ L(B(M)) we say that Ã¸1~Ã¸2, whenever for every T Ïµ B(M), Ã¸1(T) has property P...

- On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition. Kamynin, V. // Mathematical Notes;Mar/Apr2005, Vol. 77 Issue 3/4, p482
We study the unique solvability of the inverse problem of determining the righthand side of a parabolic equation whose leading coefficient depends on both the time and the spatial variable under an integral overdetermination condition with respect to time. We obtain two types of condition...

- Unit-Circle Preserving Mappings. Soon-Mo Jung; Byungbae Kim // Southeast Asian Bulletin of Mathematics;2007, Vol. 31 Issue 2, p259
We prove that if a bijective mapping f : Rn ? R n (n = 2) preserves the unit circles, then f is linear isometry up to translation.

- On the Hyers-Ulam Stability of a bi-Jensen Functional Equation. Gwang-Hui Kim; Yang-Hi Lee; Dal-Won Park // AIP Conference Proceedings;9/17/2008, Vol. 1046 Issue 1, p99
In this paper, we prove the stability of a bi-Jensen functional equation

4f( . ,x+y 2 ) = f(x,z)+f(x,w)+f(y,z)+f(y,w)z+w 2 - Binet-Cauchy Kernels on Dynamical Systems and its Application to the Analysis of Dynamic Scenes. Vishwanathan, S.; Smola, Alexander; Vidal, René // International Journal of Computer Vision;May2007, Vol. 73 Issue 1, p95
We propose a family of kernels based on the Binet-Cauchy theorem, and its extension to Fredholm operators. Our derivation provides a unifying framework for all kernels on dynamical systems currently used in machine learning, including kernels derived from the behavioral framework, diffusion...

- Semi-Fredholm problems on periodic solutions of functional-differential equations of neutral type. Antonevich, A.; Lo, S. // Differential Equations;Oct2011, Vol. 47 Issue 10, p1385
We consider the problem on periodic solutions for linear systems of functionaldifferential equations of neutral type with periodic coefficients and periodic deviations of the argument. By reduction to associated functional equations, we derive necessary and sufficient conditions under which the...

- On Pseudo-Inverses of Fredholm Operators. Schmoeger, Christoph // Turkish Journal of Mathematics;2008, Vol. 32 Issue 4, p467
Suppose that A is a Fredholm operator on a Banach space. We prove that A has index = 0 (resp. = 0, resp. = 0) if and only if A has pseudo-inverse which is invertible (resp. Fredholm and left invertible, resp. Fredholm and right invertible). Furthermore, we determine the interior points of some...

- Periodic Solutions for a Class of n-th Order Functional Differential Equations. Bing Song; Lijun Pan; Jinde Cao // International Journal of Differential Equations;2011, p1
We study the existence of periodic solutions for n-th order functional differential equations x(n)(t)=âˆ‘i=0n-1bi[x(i)(t)]k+f(x(t-Ï„(t)))+p(t). Some new results on the existence of periodic solutions of the equations are obtained. Our approach is based on the coincidence degree theory of...

- Solution of the Cauchy Problem for Two Differential-Algebraic Equations with a Fredholm Operator. Zubova, S. // Differential Equations;Oct2005, Vol. 41 Issue 10, p1486
The article analyzes a Cauchy problem for two differential-algebraic equations with a Fredholm operator. It was assumed that A is Fredholm of index zero and obtain complete conditions for the existence of solutions for the case of a regular pencil as well as for the irregular case. Cascade space...