Lattice-point generating functions for free sums of convex sets

Let \J and \K be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in \J \cap \K, and let \J \oplus \K = \conv(\J \cup \K). We give formulas for the generating function {equation*} \sigma_{\cone(\J \oplus \K)}(z_1,..., z_n, z_{n+1}) = \sum_{(m_1,..., m_n) \in t(\J \oplus \K) \cap \Z^{n}} z_1^{m_1}... z_n^{m_n} z_{n+1}^{t} {equation*} of lattice points in all integer dilates of \J \oplus \K in terms of \sigma_{\cone \J} and \sigma_{\cone \K}, under various conditions on \J and \K. This work is motivated by (and recovers) a product formula of B.\ Braun for the Ehrhart series of \P \oplus \Q in the case where $\P$ and \Q are lattice polytopes containing the origin, one of which is reflexive. In particular, we find necessary and sufficient conditions for Braun's formula and its multivariate analogue.Comment: 17 pages, 2 figures, to appear in Journal of Combinatorial Theory Series

An efficient resource sharing technique for multi-tenant databases

Multi-tenancy is one of the key components of cloud computing environment. Multi-tenant database system in SaaS (Software as a Service) has gained a lot of attention in academics, research and business arena. These database systems provide scalability and economic benefits for both cloud service providers and customers(organizations/companies referred as tenants) by sharing same resources and infrastructure in isolation of shared databases, network and computing resources with Service level agreement (SLA) compliances. In a multitenant scenario, active tenants compete for resources in order to access the database. If one tenant blocks up the resources, the performance of all the other tenants may be restricted and a fair sharing of the resources may be compromised. The performance of tenants must not be affected by resource-intensive activities and volatile workloads of other tenants. Moreover, the prime goal of providers is to accomplish low cost of operation, satisfying specific schemas/SLAs of each tenant. Consequently, there is a need to design and develop effective and dynamic resource sharing algorithms which can handle above mentioned issues. This work presents a model embracing a query classification and worker sorting technique to efficiently share I/O, CPU and Memory thus enhancing dynamic resource sharing and improvising the utilization of idle instances proficiently. The model is referred as Multi-Tenant Dynamic Resource Scheduling Model (MTDRSM) .The MTDRSM support workload execution of different benchmark such as TPC-C(Transaction Processing Performance Council), YCSB(The Yahoo! Cloud Serving Benchmark)etc. and on different database such as MySQL, Oracle, H2 database etc. Experiments are conducted for different benchmarks with and without SLA compliances to evaluate the performance of MTDRSM in terms of latency and throughput achieved. The experiments show significant performance improvement over existing Mute Bench model in terms of latency and throughput

The Hoffman-Wielandt (type) inequality for quaternion matrices and quaternion matrix polynomials

The purpose of this manuscript is to derive the Hoffman-Wielandt inequality and its most general form for quaternion matrices. Diagonalizabilty of the block companion matrix of certain quadratic (linear) quaternion matrix polynomials is brought out. As a consequence, we prove that if $Q(\lambda)$ is another quadratic (linear) quaternion matrix polynomial, then the Hoffman-Wielandt type inequality for their corresponding block companion matrices holds

Eigenvalue location of certain matrix polynomials

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < |\lambda| < 2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly stochastic matrix coefficients or Schur stable matrix coefficients also have eigenvalues in similar annular regions

Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials

Matrix polynomials with unitary/doubly stochastic coefficients form the subject matter of this manuscript. We prove that if $P(\lambda)$ is a quadratic matrix polynomial whose coefficients are either unitary matrices or doubly stochastic matrices, then under certain conditions on these coefficients, the corresponding block companion matrix $C$ is diagonalizable. Consequently, if $Q(\lambda)$ is another quadratic matrix polynomial with corresponding block companion matrix $D$, then a Hoffman-Wielandt type inequality holds for the block companion matrices $C$ and $D$. Condiagonalizability of the block companion matrix of a matrix polynomial and a Hoffman-Wielandt type inequality involving coneigenvalues are also discussed.Comment: Title of the manuscript has been changed. Few more examples are added wherever necessar

Depression treatment in individuals with cancer: a comparative analysis with cardio-metabolic conditions

A clear picture of the current state of nationwide depression treatment practices in individuals with cancer and depression does not exist in the United States (US). Therefore, the primary objective of this study was to examine rates of any depression treatment among individuals with cancer and depression in the US. To better understand the relationship between any treatment for depression and presence of cancer, we used a comparison group of individuals with cardio-metabolic conditions owing to the similar challenges faced in management of depression in individuals with these conditions. We used a retrospective cross-sectional design and data from multiple years of the Medical Expenditure Panel Survey, a nationally representative household-survey on healthcare utilization and expenditures. Study sample consisted of adults aged 21 or older with self-reported depression and cancer (n=528) or self-reported depression and diabetes, heart disease or hypertension (n=1643). Depression treatment comprised of any use of antidepres- sants and/or any use of mental health counseling services. Treatment rates for depression were 78.0% and 81.7% among individuals with cancer and cardio-metabolic conditions respectively. After controlling for socio-demographic, access-to-care, number of physician-visits, health-status, and lifestyle risk-factors related variables; individuals with cancer were less likely to report any treatment for depression (Adjusted Odds Ratio=0.67; 95% Confidence Interval=0.49, 0.92) compared to individuals with cardio-metabolic conditions (P≤0.01). Our findings highlight the possibility that competing demands may crowd out treatment for depression and that cancer diagnosis may be a barrier to depression treatment

ERMO2 algorithm: an energy efficient mobility management in mobile cloud computing system for 5G heterogeneous networks

Recently, mobile devices are becoming the primary platforms for every user who always roam around and access the cloud computing applications. Mobile cloud computing (MCC) combines the both mobile and cloud computing, which provides optimal services to the mobile users. In next-generation mobile environments, mainly due to the huge number of mobile users in conjunction with the small cell size and their portable information‟s, the influence of mobility on the network performance is strengthened. In this paper, we propose an energy efficient mobility management in mobile cloud computing (E2M2MC2) system for 5G heterogeneous networks. The proposed E2M2MC2 system use elective repeat multi-objective optimization (ERMO2) algorithm to determine the best clouds based on the selection metrics are delay, jitter, bit error rate (BER), packet loss, communication cost, response time, and network load. ERMO2 algorithm provides energy efficient management of user mobility as well as network resources. The simulation results shows that the proposed E2M2MC2 system helps in minimizing delay, packet loss rate and energy consumption in a heterogeneous network

The Smart Guide Cane for Assisting the Visually Challenged for Indoor

This paper introduces the concept of the Smart Cane that will use to guide the visually challenged person while walking. Cane is nothing but a hollow stick that is commonly used by the blind one usually. Here the cane is improved by using the sensors for obstacle detection, moisture and fire detection in their environment and to guide them towards their destination. Here we developed the hardware of the Smart Cane by using Atmega328 microcontroller and the outputs are display on the LCD

Development and Validation of Spectrophotometric and Chromatographic Method for the Estimation of Apremilast in Bulk and Formulations

Objective: Objective of the present analytical research work was to develop and validate Spectrophotometric method and High Performance Liquid Chromatographic method (HPLC Method) for the Apremilast bulk and tablets dosage form. Methods: A spectrophotometric method and a HPLC method have been developed and validated for estimation of APR in pharmaceutical oral dosage form. Method A (UV SPECTROMETRY Method): The stock and working standard solutions of the drugs were prepared in methanol. Standard solutions were scanned over the range of 400-200 nm in spectrum mode of spectrophotometer at medium scanning speed using UV spectrophotometer. The maximum absorbance for Apremilast was found at 230 nm. Method B (HPLC Method): The HPLC Method for Apremilast was developed using Cosmosil C18 (4.6mm x 250mm, Particle size: 5µm), as stationary particle, isocratic mode. Methanol: Water (80:20v/v) pH3 as mobile phase. Mobile phase was maintained at a flow rate of 0.8 ml/min and detection was carried out at 230 nm. Both the methods were validated in accordance with ICH guidelines Results: Apremilast was found to be linear in the concentration range of 2-10 µg/ml for spectrophotometric method and 10-50 µg/ml for HPLC method. Retention time was found to be 4.0 min for Apremilast. The amount of Apremilast in marketed formulation by spectrophotometric method was found to be 99.82 %, the amount of Apremilast in marketed formulation by HPLC method was found to be 99.98 %. Interpretation and Conclusion: Results of assay and validation study were found to be satisfactory. So, the methods can be successfully applied for the routine analysis of Apremilast. Keywords: HPLC, bulk dosage form, tablets