Goal: Describe the image of the cone Sn ≥� of positive semidefinite quadratic forms under the projection πG . Sn ≥�: convex cone of quadratic forms∑i , j ai jxix j such that∑i , j ai jpi p j ≥ � for all (p�, . . . , pn) ∈ Rn. Theorem (Diagonalization ofQuadratic Forms). Aquadratic form q ∈ R[x�, . . . , xn] is positive semidefinite if and only if it is a sum of squares of linear forms after a c...

إ ةيرهجملا جماربلا لمشي اذهو ،ةيرورملا ةآرحلا ةاآاحم جمارب روطت يف مهاس ةيتامولعملا ايجولونكتلا يف ريبكلا مدقتلا ن ) Microscopic ( ، نلا ىلع بلطلا ةاآاحم اًضيأ لمشي نايحلأا ضعب يفو ، تاعطاقتو قرط نم اهيف امب لقنلا ةموظنم ةاآاحمب حمسيل يللآا بساحلا تاقيبطت قاطنو لق . ةيرهجملا ةيرورملا ةآرحلا ةاآاحم جمارب نيب نراقتو عجارت ةقرولا هذهو ) Microscopic ( ةيلومشلاو ) Macroscopic ( فلاتخلاا هجوأ ىلع ةزآر...

Let X1; : : : ;Xn be n independent, symmetric random variables supported on the interval [-1,1] and let Sn = Pn i=1Xi be their sum. We show that the di erential entropy of Sn is maximized when X1; : : : ;Xn 1 are Bernoulli taking on +1 or -1 with equal probability and Xn is uniformly distributed. This entropy maximization problem is due to Shlomo Shamai [1] who also conjectured the solution1.

The Dirac operators Ly = i 1 0 0 −1 dy dx + v(x)y, y = y1 y2 , x ∈ [0, π], with L 2-potentials v(x) = 0 P (x) Q(x) 0 , P,Q ∈ L 2 ([0, π]), considered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions (bc), have discrete spectra, and the Riesz projections SN = 1 2πi |z|=N− 1 2 (z − L bc) −1 dz, Pn = 1 2πi |z−n|= 1 2 (z − L bc) −1 dz are well-defined for |n| ≥ N if N is suffi...

Mazhar (1971) gave the characterization for the series ∑ an n to be summable |N,pn|whenever ∑ an is summable |C,α|k, α≥ 0, k≥ 1. Here we prove two theorems, the first concerns the sufficient conditions and the second the necessary conditions satisfied by { n } in order to have ∑ an n summable |N̄,pn|k whenever ∑ an is summable |C,α|k, k≥ 1. 2000 Mathematics Subject Classification. Primary 40G. L...

The classical Poisson theorem says that if ξ 1 , ξ 2 , ... are i.i.d. 0– 1 Bernoulli random variables taking on 1 with probability pn ≡ λ/n then the sum Sn = n i=1 ξ i is asymptotically in n Poisson distributed with the parameter λ. It turns out that this result can be extended to sums of the form Sn = n i=1 ξ q 1 (i) · · · ξ q ℓ (i) where now pn ≡ (λ/n) 1/ℓ and 1 ≤ q 1 (i) < · · · < q ℓ (i) ar...

اهتفاقثو اهرخفو ةملأا ةيأ ةيوه نم أزجتي لا اءزج يرامعملا ثارتلا لكشي . ةيخيراتلا ةرامعلا رصانع نا يف اهؤانبو اهميمصت مت دق ةيملاسلإا تابلطتمل يويحو لاعف لكشب ةباجتسلاا ىلع ةرداق نوكت ثيحب يضاملا ةينيدلاو ةيسفنلاو ةيعامتجلااو ةيئيبلاو ةيداملا سانلا . رضاحلا تقولا يف نويرامعملا نوسدنهملا موقي رصانعلا ذخأب اوذخأي ام ةداعو ميمصتلا عيراشم يف اهلاخدا و ةيملاسلإا ةيخيراتلا ينابملا نم ةفلتخملا نيوكت ر...

Aeromonas veronii is a pathogenic gram-negative bacterium, which infects a variety of animals and results in mass mortality. The stalled-ribosome rescues are reported to ensure viability and virulence under stress conditions, of which primarily include trans-translation and alternative ribosome-rescue factor A (ArfA) in A. veronii. For identification of specific peptides that interact and inhib...

Recently Richard Stanley [3] initiated a study of the distribution of the length asn(w) of the longest alternating subsequence in a random permutation w from the symmetric group Sn. Among other things he found an explicit formula for the generating function (on n and k) for Pr (asn(w) ≤ k) and conjectured that the distribution, suitably centered and normalized, tended to a Gaussian with varianc...