The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties.
The numerical range of an n × n matrix is determined by an n degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an n degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus g = 1. We reformulate the Fiedler-Helton-Vinnikov formulae for the genus g = 0, 1, and present an elementary computation of the reformulation. Several examples are provided for computing the real symmetric matrices using the reformulation., Mao-Ting Chien, Hiroshi Nakazato., and Obsahuje seznam literatury
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if $R$ is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication $R$-modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
Příspěvek Ondřeje Maňoura je ohlédnutím za mezinárodní konferencí k výročí 100 let od založení ČSR, která se uskutečnila v Praze ve dnech 30. až 31. května 2018., Ondřej Maňour., Rubrika: Konference, and Cizojazyčné resumé není.
We show that for every $\varepsilon >0$ there is a set $A\subset \mathbb{R}^3$ such that ${\Cal H}^1\llcorner A$ is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and ${\Cal H}^1\llcorner A$ has the $1$-dimensional density between $1$ and $2+\varepsilon $ everywhere in the support.
Concentration and particle size distribution has been experimentally measured in a 2D rectangular duct under near iso-kinetic conditions for multi-sized particulate slurry. Measurements have been made at different flow velocities for various efflux concentrations in the range of 10 to 50 % by weight. It is observed that the concentration profile is highly skewed towards the bottom of the duct, which reduces with increase in efflux concentration and velocity. Similar phenomenon is observed in the distribution of individual particle size fractions with the effect being more pronounced for the coarser particles. and Rozdělení koncentrace a velikosti částic bylo měřeno ve 2D pravoúhlém kanále při proudění disperze různě velkých částic za téměř iso-kinetických podmínek. Experimenty byly provedeny při různých rychlostech s dopravními koncentracemi v rozsahu 10 až 50 hmotnostních procent. Bylo zjištěno, že koncentrační profil je výrazně zešikmený ke dnu kanálu, což se však zmenšuje s růstem koncentrace a rychlosti. Podobný jev byl pozorován u distribuce částic jednotlivých velikostních frakcí. Jev se projevuje tím výrazněji, čím větší jsou částice.
Sand-water slurry was investigated on an experimental pipe loop of inner diameter D = 100 mm with the horizontal, inclined, and vertical smooth pipe sections. A narrow particle size distribution silica sand of mean diameter 0.87 mm was used. The experimental investigation focused on the effects of pipe inclination, overall slurry concentration, and mean velocity on concentration distribution and deposition limit velocity. The measured concentration profiles showed different degrees of stratification for the positive and negative pipe inclinations. The degree of stratification depended on the pipe inclination and on overall slurry concentration and velocity. The ascending flow was less stratified than the corresponding descending flow, the difference increasing from horizontal flow up to an inclination angle of about +30°. The deposition limit velocity was sensitive to the pipe inclination, reaching higher values in the ascending than in the horizontal pipe. The maximum deposition limit value was reached for an inclination angle of about +25°, and the limit remained practically constant in value, about 1.25 times higher than that in the horizontal pipe. Conversely, in the descending pipe, the deposition limit decreased significantly with the negative slopes and tended to be zero for an inclination angle of about −30°, where no stationary bed was observed.