scholarly journals On the anti-Wick symbol as a Gelfand-Shilov generalized function

2020 ◽  
Vol 148 (7) ◽  
pp. 2909-2914
Author(s):  
L. Amour ◽  
N. Lerner ◽  
J. Nourrigat
Keyword(s):  
Generalized Function ◽  
Wick Symbol

scholarly journals Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

2021 ◽  
Vol 19 (1) ◽  
pp. 329-337
Author(s):  
Huo Tang ◽  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Function Class ◽  
Partial Sums ◽  
Generalized Function ◽  
Inclusion Relations ◽  
Alpha Beta

Abstract Let f k ( z ) = z + ∑ n = 2 k a n z n {f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f ( z ) = z + ∑ n = 2 ∞ a n z n f\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n} . In this paper, we determine sharp lower bounds for Re { f ( z ) / f k ( z ) } {\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\} , Re { f k ( z ) / f ( z ) } {\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\} , Re { f ′ ( z ) / f k ′ ( z ) } {\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re { f k ′ ( z ) / f ′ ( z ) } {\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\} , where f ( z ) f\left(z) belongs to the subclass J p , q m ( μ , α , β ) {{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean ( p , q ) \left(p,q) -differential operator. In addition, the inclusion relations involving N δ ( e ) {N}_{\delta }\left(e) of this generalized function class are considered.

Design and research of a novel type of mechanical presses driven by three servo motors in parallel

2012 ◽  
Vol 227 (3) ◽  
pp. 580-591 ◽  
Author(s):  
Xun Huang ◽  
Chunxiang Ma ◽  
Suxing Wu ◽  
Qian Wang ◽  
Zhibo Wang ◽  
...  
Keyword(s):  
Probability Theory ◽  
Forward Kinematics ◽  
Generalized Function ◽  
Engineering Practice ◽  
Drawing Process ◽  
Fuzzy Probability ◽  
Fuzzy Reliability ◽  
Deep Drawing Process ◽  
Computing Method ◽  
Fuzzy Probability Theory

A novel type of mechanical presses design driven by three servo motors in parallel is proposed to develop high stamping capacity based on the theory of generalized function sets, and then is improved to enhance its practicability in engineering practice. The inverse and forward kinematics analyses are conducted later. Based on the fuzzy probability theory, the computing method of fuzzy reliability of kinematic accuracy of slider is then obtained. Finally, with a set of optimized length parameters of the presses given, the fuzzy reliability is calculated, on the basis of which a typical deep-drawing process is simulated.

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

scholarly journals A generalized inversion formula for the continuous Jacobi transform

1987 ◽  
Vol 10 (4) ◽  
pp. 671-692 ◽  
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Analytic Function ◽  
Inversion Formula ◽  
Generalized Functions ◽  
Generalized Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Inversion ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

Implicit Function Alteration via Radius Mapping and Direct Function Modification

1995 ◽  
Author(s):  
Mark T. Ensz ◽  
Mark A. Ganter ◽  
Duane W. Storti
Keyword(s):  
Generalized Function ◽  
Implicit Function ◽  
Implicit Functions ◽  
Direct Function ◽  
Surface Features ◽  
And Function ◽  
Implicit Solid

Abstract In this paper, we present two closely related techniques, radius mapping, and direct function modification, that allow for the alteration of both the major geometry and surface features of implicit solids. The first technique, radius mapping, is applied to implicit functions generated by swept solid techniques. A more generalized technique, direct function modification, allows for the mapping of generalized function modifiers onto any implicit solid. Both the radius functions and the function modifiers can be either algebraic or non-algebraic in nature. Techniques for generating both algebraic and non-algebraic radius functions and function modifiers are given along with several examples of their use on both swept solids and implicit functions.

scholarly journals Optimization Formulation of Semi-Finished Sponge Cake

2020 ◽  
Vol 50 (1) ◽  
pp. 44-51
Author(s):  
Ekaterina Marinina ◽  
Madina Sadygova ◽  
Tatiana Kirillova ◽  
Irina Kanevskaya
Keyword(s):  
Wheat Flour ◽  
Mass Fraction ◽  
Animal Feed ◽  
Desirability Function ◽  
Control Sample ◽  
Generalized Function ◽  
Sponge Cake ◽  
Rye Flour ◽  
Local Selection ◽  
Confectionery Products

Introduction. The research improved the formulation of semi-finished sponge cake by using the method of generalized desirability function. Traditional components were substituted with new advantageous rye varieties of local selection. The main advantage of the rye variety “Memory to Bambyshev” is that rye flour obtained from the whole grain of this variety has a lower trypsin inhibitor (1.7 mg/g) compared to flour from such varieties as “Saratov 6” (2.16 mg/g). Thus, the digestibility of the grain of this variety is higher by 0.26%. The rye can be used in baking to produce dietary breads, low-calorie bakery products with bran, and animal feed. Study objects and methods. Cakes and pastries make 34.5% of the total volume of flour confectionery products. The study developed a new semi-finished sponge-cake product, which can serve as the basis for cakes and pastries. However, flour confectionery products are oversaturated with carbohydrates and fats, which increases their calorie content. A set of experiments was performed to study the effect of reducing the amount of sugar in the formulation and replacing wheat flour with rye flour on the quality of semi-finished sponge-cake product. A basic formulation for sponge cake was used as control sample. The test semples varied in content of sugar and flour made from various types of rye. The technological additives included Ovalet emulsifier (1.5% to flour) and Duo baking powder (0.1% to flour). Emulsifier “OVALET SUPER” (Bakels, Sweden) is a pasty substance that consists of emulsifying agents, water, and stabilizers and acts as an improver, stabilizer, and structurizer designed for the production of semi-finished sponge cakes, rolls, muffins, and cookies. Duo baking powder is a special highly effective tool that does not contain tartaric acid. It can be used for the production of various varieties of bread and confectionery, e.g. biscuits, rolls, gingerbread, etc. The obtained dough was easy to process. The new formulation increased the volume and color of the product, as well as slowed down the process of hardening. Results and discussion. The highest value of the generalized function of desirability belonged to the sample where white wheat flour was subsituted with 30% of rye flour and the sample with 100% of rye flour with a 40% sugar reduction. According to the specific desirability indicators, the mass fraction of moisture, the mass fraction of total sugar, energy value, and foaming ability of the semifinished product were higher than those of the control sample. Conclusion. The developed formulation and technology can expand the range of functional products.

scholarly journals Using desirability functions when making managerial decisions in the mineral resource complex

2020 ◽  
Vol 1 (2) ◽  
pp. 218-224
Author(s):  
Artem Valer’evich PONOMAREV ◽  
◽  
Lyudmila Vital’evna VLASOVA ◽  
Irina Vladislavovna PEREGON ◽  
◽  
...  
Keyword(s):  
Computer Technology ◽  
Desirability Function ◽  
Geometric Mean ◽  
Partial Function ◽  
Generalized Function ◽  
Partial Functions ◽  
Desirability Functions ◽  
Managerial Decisions ◽  
First Case ◽  
Business Entities

Relevance. The ever-growing flows of information, tight deadlines for decision-making, the need to maintain competitive positions require ranking calculations to identify leaders and promote leadership factors, ranking units of business entities according to selected criteria, etc. Reliability, visualization, and often acceleration of obtaining results predetermine the appeal to mathematical techniques. Purpose of the study: substantiation of choice of the most acceptable option of the desirability function for use in the process of making managerial decisions related to the development of subsoil resources. Research method: comparative analysis of options for calculating the desirability function, comparison method, methods of mathematical statistics. Results. Two options for calculating the desirability function are considered. The first one developed by E. Harrington, who proposed a special verbal-numerical scale, which made it possible to formalize the system of preferences of different experts. The partial function of desirability, in this case, is constructed so that it is close to "satisfactory" linear one. According to recommendations, the lower and upper boundaries of “satisfactorily” correspond to the minimum and maximum values of indicators for the available data array. There is a slightly different approach to the determination of the partial function of desirability described in a number of works. The generalized desirability function is a convolution of particular functions and is defined as the geometric mean or logarithmic mean. It is possible to use weighting factors with different significance of particular desirability functions. Comparison of various approaches is made for the conditions of management of logistics and equipment of OOO Gazpromtransgaz-Yekaterinburg. An analysis of the results shows that despite discreteness of the particular desirability functions, which in the first case lie in the range from 0.37 to 0.69, and give the entire range of values from 0 to 1 in the second one, the ratings for the generalized desirability function completely coincide with regard to determining a rating of quarterly values of industrial and economic activity. It follows that both methods of calculating partial functions are legitimate, however, the first option seems more convenient technically due to the absence of values of partial desirability functions close to zero, which complicate calculations using computer technology. A third version of the rating was also tested using calculated percentage estimates of the indicators under consideration with respect to the maximum desired value (taking into account their conversion into the relative indices). As in previous cases, the rating of countries according to the generalized function of desirability turned out to be comparable with previously calculated. Conclusions. Comparative calculations confirmed the validity of both options for finding particular desirability functions, since the ratings for the generalized desirability function coincide. The first version of the calculation is more convenient due to the lack of values of particular desirability functions close to zero, which simplifies the use of computer technology

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