Some results for non-linear elliptic problems with mixed boundary conditions

We prove existence and uniqueness results for non-linear elliptic equations with lower order terms, L¹ data, and mixed boundary conditions that include as particular cases the Dirichlet and the Neumann problems. Mathematics Subject Classification (2000) 35J25, 35D05, 35J70, 35J60     

Assignment of laser lines in an optically pumped submillimeter and near millimeter laser: (H2CO)3

A large number of emissions is obtained in the submillimeter and near millimeter range with the (H₂CO)₃ laser optically pumped by a CO₂ laser. A study of the microwave absorption spectrum of the molecule carried out simultaneously with the submm analysis allows us to assign six of the laser lines in thev ₅ excited state of the molecule and to determine the rotational constants and vibrational energy ofv ₅.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

A generalized Weiszfeld method for the multi-facility location problem

An iterative method is proposed for the K facilities location problem. The problem is relaxed using probabilistic assignments, depending on the distances to the facilities. The probabilities, that decompose the problem into K single-facility location problems, are updated at each iteration together with the facility locations. The proposed method is a natural generalization of the Weiszfeld method to several facilities.     

Raman Spectroscopy of Biological Tissues

Abstract

This article reviews some of the recent advances in Raman spectroscopy, in areas related to natural tissues and cell biology. It summarizes some of the most widely used peak frequencies and their assignments. The aim of this study is to prepare a database of molecular fingerprints, which will help researchers in defining the chemical structure of the biological tissues introducing most of the important peaks present in the natural tissues. In spite of applying different methods, there seems to be a considerable similarity in defining the peaks of identical areas of the spectra. As a result, it is believed that preparing a unique collection of the frequencies encountered in Raman spectroscopic studies can lead to significant improvements both in the quantity and quality of spectral data and their outcomes. This article is the first review of its kind to provide a precise database on the most important Raman characteristic peak frequencies for researchers aiming to analyze natural tissues by Raman spectroscopy and will especially be of considerable assistance to those who are focusing on the analysis of cancerous tissues by Raman spectroscopy.     

Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Ring inversion, structural stability and vibrational assignments of sulfolane c-C4H8SO2 and 3-sulfolene c-C4H6SO2

The structural stability of sulfolane (tetrahydrothiophene1,1-dioxide) and 3-sulfolene (dihydrothiophene1,1-dioxide) was investigated by DFT-B3LYP and ab initio MP2 calculations with 6-311+G**) basis set. The calculated symmetric ring-puckering potential of 3-sulfolene at the B3LYP level is consistent with a flat minimum that corresponds to a planar ring but at the MP2 level with a double minimum with a low barrier of about 193calmol(-1) to ring planarity in reasonable agreement with experimental results. From the calculations at the two levels of theory sulfolane was predicted to exist predominantly in the twist conformation. The vibrational wavenumbers were calculated at the MP2/6-31G** level of theory and the potential energy distributions PED among the symmetry coordinates of the normal modes were computed for the low-energy structure of the molecules. Complete vibrational assignments were provided on the basis of the calculated PED values. The experimental infrared and Raman spectra of the two molecules were compared to the calculated ones.     

Full NMR analysis of annomontine, methoxy- annomontine and N-hydroxyannomontine pyrimidine-beta-carboline alkaloids

Using modern NMR techniques, including 1H--13C and 1H--15N heteronuclear correlation experiments, the complete and unambiguous 1H, 13C, and 15N NMR chemical shift assignments of annomontine, methoxyannomontine, and N-hydroxyannomontine pyrimidine-beta-carboline alkaloids were performed. All 1H--1H scalar coupling constants and signal multiplicities were determined, and all nOe observations were also included.     

On irregular prime power divisors of the Bernoulli numbers

Let ( ) denote the usual th Bernoulli number. Let be a positive even integer where or . It is well known that the numerator of the reduced quotient is a product of powers of irregular primes. Let be an irregular pair with . We show that for every the congruence has a unique solution where and . The sequence defines a -adic integer which is a zero of a certain -adic zeta function originally defined by T. Kubota and H. W. Leopoldt. We show some properties of these functions and give some applications. Subsequently we give several computations of the (truncated) -adic expansion of for irregular pairs with below 1000.

     

A numerical method for the determination of weakly non‐hydrostatic non‐linear free surface wave propagation

A numerical method is described that may be used to determine the propagation characteristics of weakly non‐hydrostatic non‐linear free surface waves over a general, bottom topography. In shallow water of constant undisturbed depth, such waves are equivalent to the familiar cnoidal waves characterized by sharp crests and relatively flat troughs. For a certain range of parameters, these propagate without change of form by virtue of the weakly non‐hydrostatic balance in the vertical momentum equation. Effectively, this counters the tendency for the non‐linearity in a purely hydrostatic theory to lead to a continuously deforming surface wave profile. The realistic representation furnished by cnoidal wave theory of free surface waves in the shallow near‐shore zone has led to its utilization in evaluating their propagation characteristics. Nonetheless, the classic analytical theory is inapplicable to the case of wave propagation over a sloping beach or off‐shore sand bar topography. Under these conditions, a local change in form of the surface wave profile is anticipated before the waves break and knowing this is required in order to evaluate fully the propagation process. The efficacy of the numerical method is first demonstrated by comparing the solution for water of constant depth with the evaluation of the analytical solution expressed in terms of the Jacobian elliptic function cn. The general method described in the paper is then illustrated by experiments to determine the change in profile of weakly non‐hydrostatic non‐linear surface waves propagating over bed forms representative of those found in shallow coastal seas. Copyright © 2001 John Wiley & Sons, Ltd.