scholarly journals Continuous Interpolation of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

2007 ◽  
Vol 2007 ◽  
pp. 1-12
Author(s):  
E. O. Ayoola ◽  
John O. Adeyeye

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex space of solutions.

Author(s):  
D. A. Dikko

In the framework of the Hudson–Parthasarathy quantum stochastic calculus, we employ a recent generalization of the Michael selection results in the present noncommutative settings to prove that the function space of the matrix elements of solutions to discontinuous quantum stochastic differential inclusion (DQSDI) is arcwise connected.


Author(s):  
R.A. Herring

Rapid thermal annealing (RTA) of ion-implanted Si is important for device fabrication. The defect structures of 2.5, 4.0, and 6.0 MeV As-implanted silicon irradiated to fluences of 2E14, 4E14, and 6E14, respectively, have been analyzed by electron diffraction both before and after RTA at 1100°C for 10 seconds. At such high fluences and energies the implanted As ions change the Si from crystalline to amorphous. Three distinct amorphous regions emerge due to the three implantation energies used (Fig. 1). The amorphous regions are separated from each other by crystalline Si (marked L1, L2, and L3 in Fig. 1) which contains a high concentration of small defect clusters. The small defect clusters were similar to what had been determined earlier as being amorphous zones since their contrast was principally of the structure-factor type that arises due to the difference in extinction distance between the matrix and damage regions.


2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.


Author(s):  
P B Parejiya ◽  
B S Barot ◽  
P K Shelat

The present study was carried out to fabricate a prolonged design for tramadol using Kollidon SR (Polyvinyl acetate and povidone based matrix retarding polymer). Matrix tablet formulations were prepared by direct compression of Kollidon SR of a varying proportion with a fixed percentage of tramadol. Tablets containing a 1:0.5 (Drug: Kollidon SR) ratio exhibited a rapid rate of drug release with an initial burst effect. Incorporation of more Kollidon SR in the matrix tablet extended the release of drug with subsequent minimization of the burst effect as confirmed by the mean dissolution time, dissolution efficiency and f2 value. Among the formulation batches, a direct relationship was obtained between release rate and the percentage of Kollidon SR used. The formulation showed close resemblance to the commercial product Contramal and compliance with USP specification. The results were explored and explained by the difference of micromeritic characteristics of the polymers and blend of drug with excipients. Insignificant effects of various factors, e.g. pH of dissolution media, ionic strength, speed of paddle were found on the drug release from Kollidon-SR matrix. The formulation followed the Higuchi kinetic model of drug release. Stability study data indicated stable character of Batch T6 after short-term stability study.


2008 ◽  
Vol 43 (No. 3) ◽  
pp. 87-96 ◽  
Author(s):  
A. Dreiseitl

The results of evaluation of powdery mildew resistance in winter barley varieties in 285 Czech Official Trials conducted at 20 locations were analysed. Over the period, the number of varieties tested per year increased from four to seven in 1976−1985 to 53−61 in 2002−2005. To assess the resistance of varieties, only trials with sufficient disease severity were used. In 1976−2000, six varieties (1.7% of the varieties tested in the given years) ranked among resistant (average resistance of a variety in a year > 7.5) including NR-468 possessing the gene <i>Mla13</i>, KM-2099 with <i>mlo</i> and Marinka with the genes <i>Mla7</i>, <i>MlaMu2</i>. In 2001−2005, already 33 varieties (16.9%) ranked among resistant, of which Traminer possessing the genes <i>Ml(St)</i> and <i>Ml(IM9 </i> dominated. The proportion of susceptible varieties (average resistance ≤ 5.5) did not change in the two mentioned periods. Two-rowed varieties began to be tested as late as in 1990 (the first variety was Danilo), however, no difference was found in the resistance of two- and six-rowed varieties. Using an example of two pairs of varieties (Dura-Miraj and Marinka-Tiffany) with identical genes for specific resistance but with different resistance in the field, the efficiency of non-specific resistance is discussed. The resistance of domestic and foreign varieties was similar in 1994−2000; however, in 2001−2005 the difference was 0.75 point to disadvantage of domestic ones.


Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 870
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci

We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.


Author(s):  
Harald Fripertinger ◽  
Jens Schwaiger

AbstractIt was proved in Forti and Schwaiger (C R Math Acad Sci Soc R Can 11(6):215–220, 1989), Schwaiger (Aequ Math 35:120–121, 1988) and with different methods in Schwaiger (Developments in functional equations and related topics. Selected papers based on the presentations at the 16th international conference on functional equations and inequalities, ICFEI, Bȩdlewo, Poland, May 17–23, 2015, Springer, Cham, pp 275–295, 2017) that under the assumption that every function defined on suitable abelian semigroups with values in a normed space such that the norm of its Cauchy difference is bounded by a constant (function) is close to some additive function, i.e., the norm of the difference between the given function and that additive function is also bounded by a constant, the normed space must necessarily be complete. By Schwaiger (Ann Math Sil 34:151–163, 2020) this is also true in the non-archimedean case. Here we discuss the situation when the bound is a suitable non-constant function.


2013 ◽  
Vol 58 (3) ◽  
pp. 809-812 ◽  
Author(s):  
R. Dańko

Abstract The idea and experimental verification of assumptions of the integrated recycling process of matrices of uniform self-hardening moulding sands with synthetic resins, leading to obtaining moulding sands matrix of expected quality - is presented in the hereby paper. The basis of the presented process constitutes a combination of the method of forecasting averaged ignition losses of moulding sands after casting and defining the range of necessary matrix reclamation treatments in order to obtain its full recycling. Simultaneously, the empirically determined dependence of dusts amounts emitted during the reclamation process of the matrix from the given spent sand on the ignition loss values (which is the most proper assessment index of the obtained reclaimed material quality) was taken into account. The special experimental stand for investigations of the matrix recycling process was one of the elements of the conceptual approach and verification of its assumptions. The stand was equipped with the system of current on-line control of the purification degree of matrix grains from organic binder remains. The results of own investigations, allowing to combine ignition loss values of spent moulding sands after casting knocking out with amounts of dusts generated during the mechanical reclamation treatment of such sands, were utilized in the system.


2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.


1894 ◽  
Vol 1 (11) ◽  
pp. 496-499
Author(s):  
Henry H. Howorth

Mr. Deeley tells your readers that he has recently been to the summit of Mont Blanc, and has been studying the difference between névé and glacier ice. This is interesting; but we thought that a great many people had done the same thing during the last hundred years, and we thought that one of them, Forbes, had studied the famous Mountain and the phenomenoninquestion to good effect, not in a casual visit to the Alps, but in the course of many years of patient labour. Among other things we also thought he had shown that in a viscous body like ice, the slope of the upper surface necessary to make it begin to move is the same as the slope which, would be required to induce motion in the ice if its bed were inclined at an angle. He further collected considerable evidence to show what the least angle is upon which ice will begin to move. This is the slope, the least slope, available. It is nothing less than astounding to me that anyone should venture to postulate a Scand in avian ice-sheet in the North Sea until he had considered this necessary factor, and how it would operate.The Scand in avian ice-sheet was, I believe, the invention of Croll, who, sittinginhis arm-chair and endowed with a brilliant imagination, imposed upon sober science this extraordinary postulate. He did not dream of testing it by an examination of the coasts of Norway, or even of Britain, but put it forward apparently as a magnificent deduction. All deductions untested by experiment are dangerous. Thus it came about that the great monster which is said to have come from Norway, goodness knows by what mechanical process, speedily dissolved away on the application of inductive methods. Of course it still maintained its hold upon that section, of geologists who dogmatiseinprint a great deal about the Glacial period before they have ever seen a glacier at work at all; but I am speaking of those who have studied the problem inductively. First Mr. James Geikie, a disciple of Croll, was obliged to confess that this ice-sheet, which is actually said to have advanced as far as the hundred-fathom line in the Atlantic, and there presented a cliff of ice like the Antarctic continent, never can have reached the Faroes, which had an ice-sheet of their own. Next Messrs. Peach and Home were constrained to admit that no traces of it of any kind occur in the Orkneys, or in Eastern Scotland. They still maintained its presence in the Shetlands; however, this was upon evidence which is somewhat extraordinary. I do not mean the evidence as to the direction of the striation, which was so roughly handled by Mr. Milne-Home, but I mean the evidence they adduce that the boulders found on the islands are apparently all local ones, and that, contrary to the deposits of glaciers, they diminish in number as we recede from the matrix whence they were derived.


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