The definition and main results connected with Gröbner basis, Hilbert series and Anick's resolution are formulated. The method of the infinity behavior prediction of Gröbner basis in noncommu-tative case is presented. The extensions of BERGMAN package for IBM PC compatible computers are described. Let A =< X|R > be a finitely presented associative algebra over field K. Here are the main example...

Even though Privacy concerns (PC) and security concerns (SC) are acknowledged as separate constructs, many studies argue that they are related or, even worse, confused. Building upon the non-overlapping SC and PC dimensions, we propose Internet Users Information Transmission Security Concern (IUITSC) scale. We argue that the scale when used in conjunction with PC scale would cover the entire ga...

The main objective of this paper is to design and develop an automatic vehicle, fully controlled by a computer system. The vehicle designed in the present work can move in a pre-determined path and work automatically without the need of any human operator and it also controlled by human operator. Such a vehicle is capable of performing wide variety of difficult tasks in space research, domestic...

Let k be a finite field of characteristic p>0, W(k) the ring Witt vectors k, X smooth scheme over specW(k) dimension <p-1 and 0 special fiber X. In 1987, Deligne Illusie proved degeneration spectral sequence “de Hodge vers de Rham” in purely algebraic way, by constructing quasi-isomorphism at level derived categories between Rham complex with differentials. Simultaneously Fontaine Messing const...

A self-pulsing III-V/silicon laser is designed based on the Fano resonance between a bus-waveguide and micro-ring resonator, partially covered by graphene as nonlinear saturable absorption component. The reflector etched straight waveguide used one of cavity mirrors in coupling region to work with induced loss nonlinearity achieve pulsed lasing GHz repetition frequency. detailed characteristics...

The first immobilization of a pyrene-tagged chromium salen complex through π-π noncovalent interactions on reduced graphene oxide (rGO) is described. A very robust supported catalytic system obtained to promote asymmetric catalysis in repeated cycles, without loss activity or enantioselectivity. This specific behavior was demonstrated two different reactions (up ten reuses) promoted by complexe...

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

let $f: arightarrow b$ be a ring homomorphism and let $j$ be an ideal of $b$. in this paper, we investigate the transfer of the property of coherence to the amalgamation $abowtie^{f}j$. we provide necessary and sufficient conditions for $abowtie^{f}j$ to be a coherent ring.

Photonic add-drop filters are crucial components for the implementation of wavelength division multiplexing (WDM) in fiber-optic communication systems. The recent progress photonic integration has shown potential to integrate alongside high-performance building blocks on a chip construct compact and complex photonic-integrated circuits WDM. Typically, implementations based micro-ring resonators...

cutaneous metastases, which revealed three sites of signet ring cell carcinoma. A 50-year-old woman presented with painless cutaneous nodules, along with a change in bowel habit and weight loss. She had no history of rectal bleeding. Skin examination revealedmultiple nodules on the left side of her neck (●" Fig. 1a), below her right breast, onherback in a zoster-like distribution, and in the pe...