Let A be a standard graded Artinian K-algebra, with char K = 0. We prove the following. 1. A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr(z)(A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of A. 2. If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such t...

we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...

We establish existence and uniqueness results for initial-boundary value problems transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption that fields are bounded. In case where field is either nonnegative or nonpositive, can rely on similar techniques as of Cauchy problem. Conversely, general we introduce a new more technically demanding ...

A 76-year-old woman complained of abdominal pain in the right upper quadrant and fever that had been developing over the previous 10 days. On examination, she presented pain in the right upper quadrant with positive Murphy’s sign. Computed tomography showed the presence of acute cholecystitis and, as a casual finding, the presence of cholelithiasis with air in its interior (Fig. 1). The presenc...

A priori knowledge of physicochemical properties such as melting and boiling could expedite materials discovery. However, theoretical modeling from first principles poses a challenge for efficient virtual screening potential candidates. As an alternative, the tools data science are becoming increasingly important exploring chemical datasets predicting material properties. Herein, we extend mole...

FIG. 1 Crusted lesions with bullae the arrow showing level of pus (Hypopyon sign). A 5-year-old girl presented to us with complaints of exudative painful lesions on the face and upper back for 6 days. The lesions started as multiple fluid filled lesions on the face which turned turbid, ruptured, spread and involved the back. On examination, multiple pustules with level of pus (positive hypopyon...

Bipartite graphs are used to describe the generalized Schur complements of real matrices having no square submatrix with two or more nonzero diagonals. For any matrix A with this property, including any nearly reducible matrix, the sign pattern of each generalized Schur complement is shown to be determined uniquely by the sign pattern of A. Moreover, if A has a normalized LU factorization A = L...