1,050 research outputs found
On the smoothness of lexicographic points on Hilbert schemes
No full textWe study the geometry of standard graded Hilbert schemes of polynomial rings and exterior algebras. Our investigation is motivated by a famous theorem of Reeves–Stillman for the Grothendieck Hilbert scheme, which states that the lexicographic point is smooth. By contrast, we show that, in standard graded Hilbert schemes of polynomial rings and exterior algebras, the lexicographic point can be singular, and it can lie in multiple irreducible components. We answer questions of Peeva–Stillman and of Maclagan–Smith
Rational singularities of nested Hilbert schemes
No full textThe Hilbert scheme of points Hilb^n(S) of a smooth surface S is a well-studied parameter space, lying at the interface of algebraic geometry, commutative algebra, representation theory, combinatorics, and mathematical physics. The foundational result is a classical theorem of Fogarty, stating that Hilb^n(S) is a smooth variety of dimension 2n. In recent years there has been growing interest in a natural generalization of Hilb^n(S), the nested Hilbert scheme Hilb^(n1,n2)(S), which parametrizes nested pairs of zero-dimensional subschemes Z1 ⊇ Z2 of S with deg Zi = ni. In contrast to Fogarty’s theorem, Hilb^(n1,n2)(S) is almost always singular, and very little is known about its singularities. In this paper, we aim to advance the knowledge of the geometry of these nested Hilbert schemes. Work by Fogarty in the 70’s shows that Hilb(n,1)(S) is a normal Cohen–Macaulay variety, and Song more recently proved that it has rational singularities. In our main result, we prove that the nested Hilbert scheme Hilb(n,2)(S) has rational singularities. We employ an array of tools from commutative algebra to prove this theorem. Using Gröbner bases, we establish a connection between Hilb(n,2)(S) and a certain variety of matrices with an action of the general linear group. This variety of matrices plays a central role in our work, and we analyze it by various algebraic techniques, including the Kempf–Lascoux–Weyman technique of calculating syzygies, square-free Gröbner degenerations, and the Stanley–Reisner correspondence. Along the way, we also obtain results on classes of irreducible and reducible nested Hilbert schemes, dimension of singular loci, and F-singularities in positive characteristic
On Rees algebras of 2-determinantal ideals
No full textLet I be the ideal of minors of a 2 by n matrix of linear forms with the
expected codimension. In this paper we prove that the Rees algebra of I and its
special fiber ring are Cohen-Macaulay and Koszul; in particular, they are
quadratic algebras. The main novelty in our approach is the analysis of a
stratification of the Hilbert scheme of determinantal ideals. We study
degenerations of Rees algebras along this stratification, and combine it with
certain squarefree Groebner degenerations.Comment: Final version. To appear on the Journal of the London Mathematical
Societ
On the tangent space to the Hilbert scheme of points in P3
No full textIn this paper we study the tangent space to the Hilbert scheme
, motivated by Haiman's work on and by a long-standing conjecture of Brian\c{c}on and Iarrobino
on the most singular point in . For points
parametrizing monomial subschemes, we consider a decomposition of the tangent
space into six distinguished subspaces, and show that a fat point exhibits an
extremal behavior in this respect. This decomposition is also used to
characterize smooth monomial points on the Hilbert scheme. We prove the first
Brian\c{c}on-Iarrobino conjecture up to a factor of 4/3, and improve the known
asymptotic bound on the dimension of .
Furthermore, we construct infinitely many counterexamples to the second
Brian\c{c}on-Iarrobino conjecture, and we also settle a weaker conjecture of
Sturmfels in the negative.Comment: 20 pages. Final version; to appear on Transactions of the American
Mathematical Societ
Experimental evaluation of long term evolution-based NC OFDM secondary-to-secondary interference
No full textScarcity of spectrum resources, inefficient spectrum usage and the inflexibility of the current spectrum assignment are few of the major roadblocks in the development of new wireless communication standards. Secondary spectrum sharing has become a viable solution to alleviate this problem. Secondary users are unlicensed devices that use opportunistic spectrum access to identify vacant frequency bins and thereby utilize the spectrum. For advanced wireless communication standards like the Long Term Evolution (LTE) which primarily calls for higher data rates, evaluation of design parameters for ensuring efficient coexistence of heterogeneous secondary users and guaranteeing acceptable minimum level of performance becomes essential. Additionally, the understanding of the interference between secondary users occupying adjacent frequency bands for their transmission is imperative. This thesis focuses on the coexistence of secondary users in the same band assuming that the primary spectrum is found available. By Implementing two Non Contiguous Orthogonal Frequency Division Multiplexing ( NC-OFDM) based secondary transmitters on a real time platform, the design parameters that need to be considered to ensure efficient coexistence have been identified and investigated. The performance degradations observed at a particular secondary link due to presence of another interfering secondary link occupying adjacent frequency bands for its transmission have also been studied. This thesis also focuses on implementation of algorithms to modify the existing NC-OFDM transmission at the secondary transmitter end to reduce its Interference effects on the other secondary links operating within the same band. The focus is on an LTE-based Secondary Non Contiguous Orthogonal Frequency Division Multiplexing Transceiver on a Real Time Platform developed by National Instruments. The various blocks needed to design a real time LTE based communications links are discussed. An experimental LTE-to-LTE interference analysis based on the Real Time Platform and the designed system is presented.M.S.Includes bibliographical referencesby Ajay Ramkumar Iye
Enhancement of tensile strength in AA 6061-T6 plates joined by gas tungsten arc welding using high entropy alloy filler sheet
No full textThis work has focused on enhancing the tensile strength of AA 6061-T6 plates by gas tungsten arc welding (GTAW) using an AA 1100-O sheet embedded with a high entropy alloy (HEA, Cr0.14Fe0.13Al0.26Cu0.11-Si0.25Zn0.11) as a filler metal. HEA filler sheets were prepared by accumulative roll bonding (ARB). The prepared (AA 1100-O)-HEA filler metal was used to join the AA 6061-T6 plates. Phase formation and microstructural evaluations were carried out using an x-ray diffractometer and advanced electron microscopy in the (AA 6061T6)-HEA weldment. The phase evaluation results revealed the presence of HEA with Al peaks and unveiled FCC phase formations and disappearance of the BCC phase owing to the incorporation of more FCC elements and less solid dissolution. The major FCC phase is attributed to the atomic radius mismatch among the incorporated metallic elements. The retention of the HEA phase after welding indicated thermal stability and sluggish diffusion behaviour. (AA 6061-T6)-10 wt.% HEA welded plates exhibited higher strength and plasticity due to the presence of nanocrystalline HEA, superior interfacial bonding between AA 6061-T6 and HEA elements, and the involvement of solid solution (178 MPa), dislocation (152 MPa), and grain boundary strengthening (27 MPa) towards the total strength (357 MPa).11Nsciescopu
Evolution of microstructure and mechanical properties of [Cu-10Ni]-Si3N4 nanocomposites developed using mechanical alloying and spark plasma sintering
No full textThis study focused on the production of [Cu-10 Ni](x)-x wt% Si3N4 (x = 0, 3, 6, 9 and 12 wt%) nanocomposites through mechanical alloying followed by spark plasma sintering. An exhaustive exploration was carried out on the synthesised nanocrystalline/nanocomposite particles and sintered samples to study their structural characterisation and microstructural changes after 20 h of MA. The mechanical behaviour in terms of the compression test was carried out and correlated with the microstructural evaluations. The results indicated that the incorporation of Si3N4 nanoparticles decreased the matrix powder particle size considerably owing to the domination of fracturing mechanism. The results also showed that a higher strain hardening rate followed by the breaking up of the matrix powder particles occurred in the nanocomposite powders. The powder morphology of the nanocrystalline [Cu-10Ni] matrix ensured the uniform distribution of Si3N4 nanoparticles within it leading to the formation of dislocations in commensurate with the reinforcement addition. The sintered samples exhibited improved compression strength owing to the embedment of Si3N4 nanoparticles, strong bonding between the Si3N4 particles and the matrix, engendered dislocations and grain refinement. The ductility was examined and the strengthening mechanisms were computed for the deformed specimens. The results explained that the grain size, dislocation, and Orowan strengthening contributed more to the total strength and influenced the properties compared to other strengthening mechanisms. (C) 2021 Elsevier B.V. All rights reserved.11Nsciescopu
sj-docx-2-aut-10.1177_13623613231205748 – Supplemental material for Validity and feasibility of using the Modified Checklist for Autism in Toddlers, Revised with Follow-Up (M-CHAT-R/F) in primary care clinics in Singapore
No full textSupplemental material, sj-docx-2-aut-10.1177_13623613231205748 for Validity and feasibility of using the Modified Checklist for Autism in Toddlers, Revised with Follow-Up (M-CHAT-R/F) in primary care clinics in Singapore by Ruth Mingli Zheng, Siew Pang Chan, Evelyn C Law, Shang Chee Chong and Ramkumar Aishworiya in Autism</p
sj-docx-1-aut-10.1177_13623613231205748 – Supplemental material for Validity and feasibility of using the Modified Checklist for Autism in Toddlers, Revised with Follow-Up (M-CHAT-R/F) in primary care clinics in Singapore
No full textSupplemental material, sj-docx-1-aut-10.1177_13623613231205748 for Validity and feasibility of using the Modified Checklist for Autism in Toddlers, Revised with Follow-Up (M-CHAT-R/F) in primary care clinics in Singapore by Ruth Mingli Zheng, Siew Pang Chan, Evelyn C Law, Shang Chee Chong and Ramkumar Aishworiya in Autism</p
Regulation of senescence in cancer and aging
No full textCo-author Charusheila Ramkumar is a student in the Cell Biology program in the Graduate School of Biomedical Sciences (GSBS) at UMass Medical School.Senescence is regarded as a physiological response of cells to stress, including telomere dysfunction, aberrant oncogenic activation, DNA damage, and oxidative stress. This stress response has an antagonistically pleiotropic effect to organisms: beneficial as a tumor suppressor, but detrimental by contributing to aging. The emergence of senescence as an effective tumor suppression mechanism is highlighted by recent demonstration that senescence prevents proliferation of cells at risk of neoplastic transformation. Consequently, induction of senescence is recognized as a potential treatment of cancer. Substantial evidence also suggests that senescence plays an important role in aging, particularly in aging of stem cells. In this paper, we will discuss the molecular regulation of senescence its role in cancer and aging. The potential utility of senescence in cancer therapeutics will also be discussed
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