1,721,697 research outputs found
Koszul property of diagonal subalgebras
No full textLet be a polynomial ring over a field and a homogeneous ideal in generated by a regular sequence of homogeneous forms of degree~. We study a generalization of a result of Conca et al. [CHTV] concerning Koszul property of the diagonal subalgebras associated to . Each such subalgebra has the form , where . For , we extend Corollary 6.10 in [CHTV] by proving that is Koszul as soon as and . We also extend Corollary 6.10 in [CHTV] in another direction by replacing the polynomial ring with a Koszul ring
Quillen-Suslin theory for a structure theorem for the elementary symplectic group
No full textA new set of elementary symplectic elements is described. It is shown that these also generate the elementary symplectic group . These generators are more symmetrical than the usual ones, and are useful to study the action of the elementary symplectic group on unimodular rows. Also, an alternate proof of, Sp_{2n}(R)$, is shown using the Local Global Principle of D. Quillen for the new set of generators
Regular sequences of power sums and complete symmetric polynomials
Full text linkIn this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in C[x_1, x_2, . . . , x_n] for n ≥ 3 always form a regular sequence and we state the conjecture when p_a, p_b, p_c for given positive integers a < b < c forms a regular sequence in C[x_1, x_2, x_3, x_4 ].We also provide evidence for this conjecture by proving it in special instances. We also prove that any sequence of power sums of the form p_a, p_a+1 , . . ., p_a+m−1 , p_b with m < n − 1 forms a regular sequence in C[x_1, x_2, . . . , x_n ]. We also provide a partial evidence in support of conjecture’s given by Conca, Krattenthaler and Watanble in [1] on regular sequences of symmetric polynomials.<br /
A study in the context of Indo-Pak relationship (Kutch-Ran dispute)
No full textDr. Muralidhar Mandal 1, "Dharmendra Kumar Neeraj
Advances in clinical determinants and neurological manifestations of B vitamin deficiency in adults
Full text linkB vitamin deficiency is a leading cause of neurological impairment and disability throughout the world. Multiple B vitamin deficiencies often coexist, and thus an understanding of the complex relationships between the different biochemical pathways regulated in the brain by these vitamins may facilitate prompter diagnosis and improved treatment. Particular populations at risk for multiple B vitamin deficiencies include the elderly, people with alcoholism, patients with heart failure, patients with recent obesity surgery, and vegetarians/vegans. Recently, new clinical settings that predispose individuals to B vitamin deficiency have been highlighted. Moreover, other data indicate a possible pathogenetic role of subclinical chronic B vitamin deficiency in neurodegenerative diseases such as Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis. In light of these findings, this review examines the clinical manifestations of B vitamin deficiency and the effect of B vitamin deficiency on the adult nervous system. The interrelationships of multiple B vitamin deficiencies are emphasized, along with the clinical phenotypes related to B vitamin deficiencies. Recent advances in the clinical determinants and diagnostic clues of B vitamin deficiency, as well as the suggested therapies for B vitamin disorders, are described
INTERLINK: A Digital Twin-Assisted Storage Strategy for Satellite-Terrestrial Networks
Full text linkRecently, low-orbit satellite networks have gained lots of attention from society due to their wide coverage, low transmission latency, and storage and computing capacity. Providing seamless connectivity to users in different areas is envisioned as a promising solution, especially in remote areas and for marine communication. However, when jointly used with terrestrial networks composing satellite-terrestrial networks (STNs), the satellite moving speed is much faster than the ground terminal, which can cause inconsistent service from a single satellite, and therefore lead to frequent satellite handover. Moreover, due to the dynamic and time slot visibility of satellites, the topology of an intersatellite changes frequently, which results in loops during satellite handover, thereby reducing the utilization of links. To address these problems, we propose a digital twin-assisted storage strategy for satellite-terrestrial networks (INTERLINK), which leverages the digital twins (DTs) to map the satellite networks to virtual space for better communication. Specifically, we first propose a satellite storage-oriented handover scheme (ASHER) to minimize the handover frequency by considering the limited access time and capacity constraints of satellites. Then, a multiobjective optimization problem is formulated to obtain the optimal satellite by genetic algorithm. Finally, considering the timing visibility of satellite links, a digital twin-assisted intersatellite routing scheme (ITO) is introduced to improve the quality of data delivery between satellites
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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