LOCALLY AND COLOCALLY FACTORABLE BANACH SPACES

We generalize the concept of locality (resp. colocality) to the concept of locally factorable (resp. colocally factorable) such that Theorem 2 of [2] and Theorems 1.7 and 1.16 of [11] are still valid for the new concepts. In addition we show that locally factorable and colocally factorable are inherited by complemented subspace, then we present some examples and establish relations between locally factorable and colocally factorable. We prove some relations between being finitely (resp. cofinitely) represented in a Banach space and being locally factorable (resp. colocally factorable) some family of finite dimensional Banach spaces.</p

Colocality and twisted sums of Banach spaces

Using the relation between subspaces of Banach spaces and quotients of their duals, we introduce the concept of colocality to give a new method that guarantees the existence of nontrivial twisted sums in which finite quotients play a major role (Theorem 1.7). An interesting point is that no restrictions are imposed on the quotients, only on the various subspaces. New examples of nontrivial twisted sums are given.C

The influence of Karst Aquifer mineralogy and geochemistry on groundwater characteristics: West Bank, Palestine

This work reports, for the first time, the mineralogical and geochemical characteristics of karst aquifers in the Central West Bank (CWB) catchment in Palestine. It provides an integrated study approach by correlating the geochemistry of the lithology and hydrochemical data of groundwater samples. Mineralogical analysis showed that all of the samples were dominantly composed of either calcite CaCO3 (5–100 wt. %) or dolomite CaMg(CO3)2 (4–100 wt. %), with minor amounts of quartz and feldspar, which is supported by the inorganic carbon content (9–13 wt. %) and hydrochemical composition of the spring water samples. The whole-rock geochemical data indicated that the samples have low contents of trace elements and transition metals. In contrast, the concentrations of alkaline earth elements (Mg, Ca, Sr, Ba) and Mn were high in the rock and groundwater samples. Generally, the trace elements of rock samples with concentrations >10 ppm included Sr (17–330 ppm), Mn (17–367 ppm), Ba (2–32 ppm), W (5–37 ppm), Cr (3–23 ppm), Zn (1.7–28 ppm), V (4–23 ppm), and Zr (1–22 ppm), while the concentrations of all the other trace elements was below 10 ppm. Ionic ratios and hierarchical cluster analysis (HCA) suggested that the chemical evolution of groundwater was mainly related to the geogenic (rock–water) interaction in the study area. This is clear in the alkaline earth elements (Mg, Ca, Sr, Ba) ratios, especially regarding the Sr values. The calcite rock samples had higher Sr (mean 160 ppm, n = 11) than those of the dolomite rocks (mean 76 ppm, n = 9)

On the Multiwavelets Galerkin Solution of the Volterra–Fredholm Integral Equations by an Efficient Algorithm

We develop the multiwavelet Galerkin method to solve the Volterra–Fredholm integral equations. To this end, we represent the Volterra and Fredholm operators in multiwavelet bases. Then, we reduce the problem to a linear or nonlinear system of algebraic equations. The interesting results arise in the linear type where thresholding is employed to decrease the nonzero entries of the coefficient matrix, and thus, this leads to reduction in computational efforts. The convergence analysis is investigated, and numerical experiments guarantee it. To show the applicability of the method, we compare it with other methods and it can be shown that our results are better than others

An Efficient Algorithm for Solving Hyperbolic Partial Differential Equations with a Nonlocal Conservation Condition

In this paper, a numerical scheme based on the Galerkin method is extended for solving one-dimensional hyperbolic partial differential equations with a nonlocal conservation condition. To achieve this goal, we apply the interpolating scaling functions. The most important advantages of these bases are orthonormality, interpolation, and having flexible vanishing moments. In other words, to increase the accuracy of the approximation, we can individually or simultaneously increase both the degree of polynomials (multiplicity r) and the level of refinement (refinement level J). The convergence analysis is investigated, and numerical examples guarantee it. To show the ability of the proposed method, we compare it with existing methods, and it can be confirmed that our results are better than them

A Novel and Efficient Numerical Algorithm for Solving 2D Fredholm Integral Equations

A novel and efficient numerical method is developed based on interpolating scaling functions to solve 2D Fredholm integral equations (FIE). Using the operational matrix of integral for interpolating scaling functions, FIE reduces to a set of algebraic equations that one can obtain an approximate solution by solving this system. The convergence analysis is investigated, and some numerical experiments confirm the accuracy and validity of the method. To show the ability of the proposed method, we compare it with others