Well-posed problems for the fractional Laplace equation with integral boundary conditions

In this remark we study the boundary-value problems for a fractional analogue of the Laplace equation with integral boundary conditions in rectangular and half-strip domains. We prove the existence and uniqueness of solutions by using the spectral decomposition method

Nonharmonic analysis of boundary value problems

In this paper we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements of a non-self-adjoint distribution theory and the corresponding biorthogonal Fourier analysis. We give applications of the developed analysis to obtain a-priori estimates for solutions of operators that are elliptic within the constructed calculus.Comment: 54 pages, updated version, to appear in IMR

On transparent boundary conditions for the high--order heat equation

In this paper we develop an artificial initial boundary value problem for the high-order heat equation in a bounded domain $\Omega$. It is found an unique classical solution of this problem in an explicit form and shown that the solution of the artificial initial boundary value problem is equal to the solution of the infinite problem (Cauchy problem) in $\Omega$.Comment: 9 page

The Fourier transform and convolutions generated by a differential operator with boundary condition on a segment

We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator $L.$ The convolution is closely connected to the inverse operator or to the resolvent. So, we first find a representation for the resolvent, and then introduce the required convolution.Comment: 15 page

23 years of the discovery of Helicobacter pylori: Is the debate over?

The Gram negative curved bacillus H. pylori has become the prize bug of all times. Barry Marshall and Robin Warren the two discoverers of this organism have been awarded with this year's Nobel Prize. The Nobel committee at the Karolinska Institute of Sweden has selected this paradigm shift discovery of 1982 as the most impacting in medical sciences. This award has surprised many as the Nobel assembly has selected this 'Robert Koch styled medical detective work' for the prize as compared to many outstanding basic research stories on the waitlist. This editorial briefly touches the significant impact of H. pylori on gastroduodenal management and the path forward as the bug has become quite controversial in recent times

A Simple Approach to Ascertain the Magnitudes of the Coefficients of 2 p-Atomic Orbitals in Each 1t-Electron Molecular Orbital of the Linear Polyenes or Polyenyl Systems

A simple approach is suggesred to ascertain the magnitudes o[the coefficients o[all interacting 2p-atomic orbitals (2pAO) in each Tt-eledron moleeuw.r arbital o[the linearpolyenes ar polyenyl systems, C.H,.2' with n ranging from 2 to 2