An entropy based proof of the Moore bound for irregular graphs

We provide proofs of the following theorems by considering the entropy of random walks: Theorem 1.(Alon, Hoory and Linial) Let G be an undirected simple graph with n vertices, girth g, minimum degree at least 2 and average degree d: Odd girth: If g=2r+1,then n \geq 1 + d*(\Sum_{i=0}^{r-1}(d-1)^i) Even girth: If g=2r,then n \geq 2*(\Sum_{i=0}^{r-1} (d-1)^i) Theorem 2.(Hoory) Let G = (V_L,V_R,E) be a bipartite graph of girth g = 2r, with n_L = |V_L| and n_R = |V_R|, minimum degree at least 2 and the left and right average degrees d_L and d_R. Then, n_L \geq \Sum_{i=0}^{r-1}(d_R-1)^{i/2}(d_L-1)^{i/2} n_R \geq \Sum_{i=0}^{r-1}(d_L-1)^{i/2}(d_R-1)^{i/2}Comment: 6 page

The Quantum Complexity of Set Membership

We study the quantum complexity of the static set membership problem: given a subset S (|S| \leq n) of a universe of size m (m \gg n), store it as a table of bits so that queries of the form `Is x \in S?' can be answered. The goal is to use a small table and yet answer queries using few bitprobes. This problem was considered recently by Buhrman, Miltersen, Radhakrishnan and Venkatesh, where lower and upper bounds were shown for this problem in the classical deterministic and randomized models. In this paper, we formulate this problem in the "quantum bitprobe model" and show tradeoff results between space and time.In this model, the storage scheme is classical but the query scheme is quantum.We show, roughly speaking, that similar lower bounds hold in the quantum model as in the classical model, which imply that the classical upper bounds are more or less tight even in the quantum case. Our lower bounds are proved using linear algebraic techniques.Comment: 19 pages, a preliminary version appeared in FOCS 2000. This is the journal version, which will appear in Algorithmica (Special issue on Quantum Computation and Quantum Cryptography). This version corrects some bugs in the parameters of some theorem

Surface structure of Quark stars with magnetic fields

We investigate the impact of magnetic fields on the electron distribution in the electrosphere of quark stars. For moderately strong magnetic fields $B\sim 10^{13}$G, quantization effects are generally weak due to the large number density of electrons at surface, but can nevertheless affect the spectral features of quark stars. We outline the main observational characteristics of quark stars as determined by their surface emission, and briefly discuss their formation in explosive events termed Quark-Novae, which may be connected to the $r$-process.Comment: 9 pages, 3 figures. Contribution to the proceedings of the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9), Bhubaneswar, India, 3-14 Jan. 200

Quark Matter in Neutron Stars: An apercu

The existence of deconfined quark matter in the superdense interior of neutron stars is a key question that has drawn considerable attention over the past few decades. Quark matter can comprise an arbitrary fraction of the star, from 0 for a pure neutron star to 1 for a pure quark star, depending on the equation of state of matter at high density. From an astrophysical viewpoint, these two extreme cases are generally expected to manifest different observational signatures. An intermediate fraction implies a hybrid star, where the interior consists of mixed or homogeneous phases of quark and nuclear matter, depending on surface and Coulomb energy costs, as well as other finite size and screening effects. In this brief review article, we discuss what we can deduce about quark matter in neutron stars in light of recent exciting developments in neutron star observations. We state the theoretical ideas underlying the equation of state of dense quark matter, including color superconducting quark matter. We also highlight recent advances stemming from re-examination of an old paradigm for the surface structure of quark stars and discuss possible evolutionary scenarios from neutron stars to quark stars, with emphasis on astrophysical observations.Comment: 15 pages, 1 figure. Invited review for Modern Physics Letters

Cholesterol Behind the Whole Life of Humans

Cholesterol is a sterol, synthesized by animal cells and vital lipid molecule for human cells (animal) and is also a component of the diet, being present in food of animal origin. Its main function is to maintain the integrity and fluidity of cell membranes and to serve as a precursor for the synthesis of substance that are vital for the organism including steroid hormones, bile acids and vitamin D. animal cells acquire cholesterol from extracellular lipoprotein and form new synthesis of cells. Dietary cholesterol comes exclusively from animal sources, it is naturally present in our diet and tissues. Cholesterol is synthesized in the human body in order to maintain a stable peel when dietary intake is low, given the necessity for cholesterol, very effective intestinal uptake mechanisms bile acid and cholesterol reabsorption cycles exist1. Conversely carbohydrates are poorly absorbed and indeed rapidly excreted. Dietary cholesterol content does not significantly influence cholesterol value, which are regulated by various nutritional. Factors that influence cholesterol absorption (or) synthesis. Recent study data do not support a link between dietary cholesterol and cardio vascular diseases2

Constraining phases of quark matter with studies of r-mode damping in neutron stars

The r-mode instability in rotating compact stars is used to constrain the phase of matter at high density. The color-flavor-locked phase with kaon condensation (CFL-K0) and without (CFL) is considered in the temperature range 10^8K < T <10^{11} K. While the bulk viscosity in either phase is only effective at damping the r-mode at temperatures T > 10^{11} K, the shear viscosity in the CFL-K0 phase is the only effective damping agent all the way down to temperatures T > 10^8 K characteristic of cooling neutron stars. However, it cannot keep the star from becoming unstable to gravitational wave emission for rotation frequencies f ~ 56-11 Hz at T ~ 10^8-10^9 K. Stars composed almost entirely of CFL or CFL-K0 matter are ruled out by observation of rapidly rotating neutron stars, indicating that dissipation at the quark-hadron interface or nuclear crust interface must play a key role in damping the instability.Comment: 8 pages, 2 figure

Freight Management in Logistic Sector Using Android

Logistics plays a major role in transforming a developing country to developed country. Since the business sector becomes very competitive, establishing communications between the customers and transporters is very important. This gives rise to a high economic status. Nowadays various difficulties such as unreliable load delivery, unorganized logistic sector etc. are encountered during transportation of goods in business communication. To ease these complexities faced by load owners in the transportation sector, an innovative mobile app has been developed; in turn, addressing the inefficiencies and fragments plays a major role in the unorganized logistics sector. This mobile app achieves transparency, standardization and reliability in the transportation industry. The work is implemented right from vendor selection, assigning vendors to carry load, matching the right trucks for different load requirements to monitoring load, handling payments till the depth of entire transportation. The proposed work carries out the transportation workflow and personally addresses them using technology to deliver the promise of shipment from its origin to destination in a reliable way with great customer service throughout.

On χs-Orthogonal Matrices

In this paper we, introduced the concept of χs-orthogonal matrices and extended some results of Abaraetal, [3] in the context of secondary transpose

Magnetar oscillations pose challenges for strange stars

Compact relativistic stars allow us to study the nature of matter under extreme conditions, probing regions of parameter space that are otherwise inaccessible. Nuclear theory in this regime is not well constrained: one key issue is whether neutron stars are in fact composed primarily of strange quark matter. Distinguishing the two possibilities, however, has been difficult. The recent detection of seismic vibrations in the aftermath of giant flares from two magnetars (highly magnetized compact stars) is a major breakthrough. The oscillations excited seem likely to involve the stellar crust, the properties of which differ dramatically for strange stars. We show that the resulting mode frequencies cannot be reconciled with the observations for reasonable magnetar parameters. Ruling out strange star models would place a strong constraint on models of dense quark matter.Comment: Parameter space expanded, 5 pages, 3 figures, MNRAS Letters in pres

Explicit deterministic constructions for membership in the bitprobe model

We look at time-space tradeoffs for the static membership problem in the bit-probe model. The problem is to represent a set of size up to n from a universe of size m using a small number of bits so that given an element of the universe, its membership in the set can be determined with as few bit probes to the representation as possible. We show several deterministic upper bounds for the case when the number of bit probes, is small, by explicit constructions, culminating in one that uses o(m) bits of space where membership can be determined with [lg lgn] + 2 adaptive bit probes. We also show two tight lower bounds on space for a restricted two probe adaptive scheme