Generalized weighted Birkhoff–Young quadratures with the maximal degree of exactness

2017 ◽  
Vol 116 ◽  
pp. 238-255 ◽  
Author(s):  
Gradimir V. Milovanović
Keyword(s):  
Maximal Degree ◽  
Degree Of Exactness

scholarly journals Non-defectivity of Grassmannian bundles over a curve

2016 ◽  
Vol 27 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundles ◽  
Manuscripta Math ◽  
Maximal Degree ◽  
Geometric Proof ◽  
Secant Varieties ◽  
Grassmann Bundle ◽  
Positive Rank

Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on vector bundles over a curve, Manuscripta Math. 133 (2010) 465–477, I. Choe and G. H. Hitching, Lagrangian sub-bundles of symplectic vector bundles over a curve, Math. Proc. Cambridge Phil. Soc. 153 (2012) 193–214]. From the non-defectivity, we also deduce an interesting feature of a general orthogonal bundle of even rank over [Formula: see text], contrasting with the classical and symplectic cases: a general maximal isotropic sub-bundle of maximal degree intersects at least one other such sub-bundle in positive rank.

scholarly journals A certain class of quadratures with even Tchebychev weights

2012 ◽  
Vol 20 (1) ◽  
pp. 447-458
Author(s):  
Zlatko Udovičić ◽  
Mirna Udovičić
Keyword(s):  
Weight Function ◽  
Algebraic Degree ◽  
Quadrature Formulas ◽  
Approximate Computation ◽  
Degree Of Exactness

Abstract We are considering the quadrature formulas of “practical type” (with five knots) for approximate computation of integral [xxx] where w(·) denotes (even) Tchebychev weight function. We prove that algebraic degree of exactness of those formulas can not be greater than five. We also determined some admissible nodes and compared proposed formula with some other quadrature formulas.

scholarly journals Clique coverings of graphs V: maximal-clique partitions

1982 ◽  
Vol 25 (3) ◽  
pp. 337-356 ◽  
Author(s):  
N.J. Pullman ◽  
H. Shank ◽  
W.D. Wallis
Keyword(s):  
Maximal Clique ◽  
Maximal Degree ◽  
Open Problems ◽  
Partition Number

A maximal-clique partition of a graph G is a way of covering G with maximal complete subgraphs, such that every edge belongs to exactly one of the subgraphs. If G has a maximal-clique partition, the maximal-clique partition number of G is the smallest cardinality of such partitions. In this paper the existence of maximal-clique partitions is discussed – for example, we explicitly describe all graphs with maximal degree at most four which have maximal-clique partitions - and discuss the maximal-clique partition number and its relationship to other clique covering and partition numbers. The number of different maximal-clique partitions of a given graph is also discussed. Several open problems are presented.

Validated RP-HPLC Method for the Estimation of Amiloride and Hydrochlorothiazide in Combined Tablet Dosage Form

2021 ◽  
pp. 316-320
Author(s):  
R. Anantha Kumar ◽  
G. Raveendra Babu ◽  
Sowjanya M. ◽  
Ramayyappa M.
Keyword(s):  
Limit Of Detection ◽  
Hplc Method ◽  
Simultaneous Estimation ◽  
Liquid Chromatographic Method ◽  
Limit Of Quantitation ◽  
Degree Of Exactness ◽  
Phase Liquid ◽  
High Degree ◽  
Tablet Dosage ◽  
Liquid Chromatographic

The aim of this work is to build up a rapid, exact, precise and accurate reverse phase liquid chromatographic method for the simultaneous analysis of amiloride and hydrochlorothiazide in tablet dose structure. The chromatographic strategy was normalized utilizing Hypersil ODS coulmn (250×4.6mm, 5μm molecule size) with UV detection at 210nm and flow rate of 1ml/min. The mobile phase includes phosphate buffer (pH acclimated to 2.5 with dilute Ortho Phosphoric acid) and acetonitrile in the proportion of 60:40 v/v. The linearity of proposed technique was found in the range of 5-30μg/ml (R²=0.999) for amiloride and 50-300μg/ml (R²=0.999) for Hydrochlorothiazide appropriately. The limit of detection (LOD) was discovered to be 0.10μg/ml and 0.40μg/ml for Amiloride and Hydrochlorothiazide appropriately. The limit of quantitation (LOQ) was discovered to be 0.30μg/ml and 1.20μg/ml for Amiloride and Hydrochlorothiazide separately. The retention times of Amiloride and Hydrochlorothiazide were found to be 3.258min and 2.383min separately. The technique was truly recommended and %RSD was found to be under 2 demonstrating high degree of exactness and accuracy. Subsequently proposed strategy can be effectively evaluated for the simultaneous estimation of Amiloride and Hydrochlorothiazide in promoted formulations.

scholarly journals Improved Resource State for Verifiable Blind Quantum Computation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 996
Author(s):  
Qingshan Xu ◽  
Xiaoqing Tan ◽  
Rui Huang
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Maximal Degree ◽  
Recent Advances ◽  
Quantum Computations ◽  
Blind Quantum Computation ◽  
Computation Graph ◽  
Resource State

Recent advances in theoretical and experimental quantum computing raise the problem of verifying the outcome of these quantum computations. The recent verification protocols using blind quantum computing are fruitful for addressing this problem. Unfortunately, all known schemes have relatively high overhead. Here we present a novel construction for the resource state of verifiable blind quantum computation. This approach achieves a better verifiability of 0.866 in the case of classical output. In addition, the number of required qubits is 2N+4cN, where N and c are the number of vertices and the maximal degree in the original computation graph, respectively. In other words, our overhead is less linear in the size of the computational scale. Finally, we utilize the method of repetition and fault-tolerant code to optimise the verifiability.

scholarly journals Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2020043-2020044
Author(s):  
Gradimir V. Milovanović ◽  
Aleksandar S. Cvetković ◽  
Marija P. Stanić
Keyword(s):  
Quadrature Formulae ◽  
Degree Of Exactness

scholarly journals VII. The David Ferrier Lecture - On some correlations between skull and brain

1932 ◽  
Vol 221 (474-482) ◽  
pp. 391-429 ◽  
Keyword(s):  
Nervous System ◽  
Structure And Function ◽  
National Tradition ◽  
Degree Of Exactness ◽  
And Function ◽  
The Brain ◽  
Made In

Mr . President and Gentlemen, My most pleasant duty to-day is to thank your Council for the honour that it has conferred upon me by inviting me to give the second lecture in memory of the late Sir David Ferrier. I have accepted this invitation with feelings of gratitude, not only to your Council, but also for the contributions made in this country to our knowledge of the structure and function of the nervous system. Among these, the works of Sir David Ferrier, however prominent, only stand out as a conspicuous example of a national tradition, maintained in recent years, both in the Physiology and Anatomy of the brain. The task I have accepted is not an easy one, the less so as the first Ferrier lecture was given by Sir Charles Sherrington who, in both the methods and results of his investigations, attained a degree of exactness at which morphologists aim in vain.

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