In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

These notes record seven lectures given in the computer algebra course in the fall of 2004. The theory of subresultants is not required for the final exam due to its complicated constructions. 1 Chinese remainder algorithm 1.1 Modular arithmetic Let m be a positive integer greater than one. We discuss basic operations in Z/(m). The elements in Z/(m) can be represented in two ways: • {0, 1, . . ...

In this lecture, we describe an approximation algorithm to the Closest Vector Problem (CVP). This algorithm, known as the Nearest Plane Algorithm, was developed by L. Babai in 1986. It obtains a 2( 2 √ 3 ) approximation ratio, where n is the rank of the lattice. In many applications, this algorithm is applied for a constant n; in such cases, we obtain a constant approximation factor. One can de...

BACKGROUND The focus of this study is on the antibacterial properties of silver nanoparticles embedded within a zeolite membrane (AgNP-ZM). METHODS AND RESULTS These membranes were effective in killing Escherichia coli and were bacteriostatic against methicillin-resistant Staphylococcus aureus. E. coli suspended in Luria Bertani (LB) broth and isolated from physical contact with the membrane ...

Nonredox type 5-lipoxygenase (5-LO) inhibitors, such as ZM 230487, its methyl analogue ZD 2138, or the Merck compound L-739,010, suppress cellular leukotriene synthesis of ionophore stimulated granulocytes with IC50 values of about 50 nM. However, in cell homogenates or in preparations of purified enzyme, up to 150-fold higher concentrations are required for similar inhibition of 5-LO activity....

We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(m logα(m,n)) time, where α is the inverse-Ackermann function. This improves upon a long standing bound of O(mα(m,n)) established by Tarjan. Our algorithms are based on an efficient split-findmin data structure, which maintains a collection of sequences of weighted eleme...

Zataria multiflora (ZM) is a thyme-like aromatic plant in the Lamiaceae family that grows in central and southern Iran. ZM is extensively used as a flavor ingredient in a wide variety of foods and is used as part of popular traditional folk remedies. In the present study, ZM essential oil (ZMO) was obtained from ZM leaves via hydro-distillation and then analyzed by GC-MS (gas chromatography-mas...

Content Based Image Retrieval (CBIR) systems based on shape using invariant image moments, viz., Moment Invariants (MI) and Zernike Moments (ZM) are available in the literature. MI and ZM are good at representing the shape features of an image. However, non-orthogonality of MI and poor reconstruction of ZM restrict their application in CBIR. Therefore, an efficient and orthogonal moment based C...

We construct a quotient ring of the ring of diagonal coinvariants of the complex reflection group W = G(m, 1, n) and determine its graded character. This generalises a result of Gordon for Coxeter groups. The proof uses a study of category O for the rational Cherednik algebra of W , including a shift isomorphism which is proved in Appendix 1.

light is never being distributed homogeneously and it forms a gradient over biomass. the unidirectional nature of light gives rise to a vertical gradient of light intensity as a function of depth. the maximum depth of the light zone suitable for phytoplankton photosynthesis is designated as the euphotic depth. this study was designed to test the hypothesis of mixing depth of phytoplankton and i...