scholarly journals Hyperbolic polynomials and linear-type generating functions

2020 ◽  
Vol 488 (2) ◽  
pp. 124085
Author(s):  
Tamás Forgács ◽  
Khang Tran
Author(s):  
R. Stavetska ◽  
Y. Dynko ◽  
M. Bushtruk ◽  
I. Starostenko ◽  
O. Babenko ◽  
...  

It has been experimentally proven that the strength and direction of the connection between the linear type traits evaluation of the Ukrainian black-and-white dairy breed cows and their body build depends on the type of the build and the sign of the exterior. The study was conducted in 2018 on a breeding plant of the Ukrainian Black-and-White Dairy breed SPC named Shchorsa in Kiev region (n=89). Differentiation of cows on types of their body build was conducted by the method proposed by Chernenko (low-capacity, mid-capacity and high-capacity types) and Kolesnik (by the massiveness index – on the friable and dense, the bone index – delicate and rough, the wide-breast and wide-rump indices – on narrow-body and wide-body types). It was found that the cow-heiferswere well-developed, had intermediate stature and optimum body condition score, deep body, and wide, slight slope rump. They alsohad desirable rear legs, set and foot angle but some toe-out, the udder was well-balanced. Under the good total score of the exterior of studied cows there were some animals with short stature (134– 136 cm), very wide rump, straight rear legs side view and toe-out, extremely steep foot angle, loose fore udder attachment, deep udder below hocks and front teat placement inside of quarter. The degree of development of the studied linear traits of cow-heifers confirms their in-herd variability. The variability of the exterior traits varies from 10,7 % (body depth) to 38,6 % (stature). In addition to the stature of a significant variability was characterized of angularity (22,4 %), rear legs set (22,5 %), body condition score (21,8 %), as well as traits that describe udder: rear udder attachment (31,4 %), udder depth (32,6 %) and front and rear teat position (31,3 % and 25,1 %, respectively). The high variability of linear traits indicates the possibility of effective their selection. As a result of the research, it has been established that the strength and direction of the correlations between the linear type traits evaluation of Ukrainian Black-and-White Dairy breed cows and the type of their body build depends on the type of the body build and the linear trait. The low-, mid- and high-capacity bodies build types (according to Chernenko) reliably correlate with chest width (r=0,58) and body depth (r=0,48), rear legs rear view (r=0,30), the central ligament (r=0,28), udder depth (r =-0,22) and teat length (r=0,25), P˂0,01–0,001. Friable and dense bodies build (according to Kolesnik) were most strongly associated with stature (r=-0,28), chest width (r =-0,70), and body depth (r=-0,38), as well as with rear legs rear view (r=-0,23), P˂0,05...0,001; delicate and rough bodies build – with stature (r=-0,51), angularity (r=-0,22),rump width (r=-0,35), udder depth (r=-0,27) and rear udder attachment (r =0,20), P ˂ 0,05–0,001; narrow-body and wide-body types – with chest width (r=0,30) and rump width (r=0,23), P˂0,05–0,01. Linear type trait evaluation of cows depends on the body build. The strength and direction of the correlations between types of body build and linear traits showed that the most informative is the classification of the body build by low-, mid- and high-capacity according to Chernenko – on the average η2x=17,5 %. The less informative – by narrow-body and wide-body types according to Kolesnik – η2x=7,6 %. The classification of cows on delicate-rough, narrow-body and wide-body types (according to Kolesnik) according to informativeness and reliability can have the intermediate position – η2x=10,0–11,5 %. The strongest influence on the body build has the cows’ height (η2x=27,9 % on average for all studied types of body build), chest width (η2x=33,5 %), body depth (η2x=21,8 %), rump width (η2x=24,1 %) and rear legs (η2x=18,7 %). Key words: cows, linear type trait evaluation, body build, correlation, power of influence.


2020 ◽  
Vol 92 (7) ◽  
pp. 85-89
Author(s):  
L. P. Mendeleeva ◽  
I. G. Rekhtina ◽  
A. M. Kovrigina ◽  
I. E. Kostina ◽  
V. A. Khyshova ◽  
...  

Our case demonstrates severe bone disease in primary AL-amyloidosis without concomitant multiple myeloma. A 30-year-old man had spontaneous vertebral fracture Th8. A computed tomography scan suggested multiple foci of lesions in all the bones. In bone marrow and resected rib werent detected any tumor cells. After 15 years from the beginning of the disease, nephrotic syndrome developed. Based on the kidney biopsy, AL-amyloidosis was confirmed. Amyloid was also detected in the bowel and bone marrow. On the indirect signs (thickening of the interventricular septum 16 mm and increased NT-proBNP 2200 pg/ml), a cardial involvement was confirmed. In the bone marrow (from three sites) was found 2.85% clonal plasma cells with immunophenotype СD138+, СD38dim, СD19-, СD117+, СD81-, СD27-, СD56-. FISH method revealed polysomy 5,9,15 in 3% of the nuclei. Serum free light chain Kappa 575 mg/l (/44.9) was detected. Multiple foci of destruction with increased metabolic activity (SUVmax 3.6) were visualized on PET-CT, and an surgical intervention biopsy was performed from two foci. The number of plasma cells from the destruction foci was 2.5%, and massive amyloid deposition was detected. On CT scan foci of lesions differed from bone lesions at multiple myeloma. Bone fragments of point and linear type (button sequestration) were visualized in most of the destruction foci. The content of the lesion was low density. There was no extraossal spread from large zones of destruction. There was also spontaneous scarring of the some lesions (without therapy). Thus, the diagnosis of multiple myeloma was excluded on the basis based on x-ray signs, of the duration of osteodestructive syndrome (15 years), the absence of plasma infiltration in the bone marrow, including from foci of bone destruction by open biopsy. This observation proves the possibility of damage to the skeleton due to amyloid deposition and justifies the need to include AL-amyloidosis in the spectrum of differential diagnosis of diseases that occur with osteodestructive syndrome.


2017 ◽  
Vol 54 ◽  
pp. 112-119
Author(s):  
L. M. Khmelnychy

The estimation of the first-born cows of Ukrainian Black-and-White dairy breed by the exterior type in the leading breeding herds of Cherkassy region by the method of linear classification (n = 566) has been carried out. The results of the evaluated animals by the 100-score system indicate that within the group of traits, the average level of assessment is "good with the plus". The animals have been differed by the good development of group features characterizing the dairy type (82.4 score), body condition (83.5 score), limbs (82.8 score), udder (82.7 score) and overall score (82.8 score). The degree of development 18 descriptive traits of the exterior of cows, has been predicted by the method of linear classification, indicates their significant intraherd variability. Animals have the moderate height, deep body and angularity. The rump angle, the angle of hock joint and the teats length, according to the variability of scores in the range of 17.8–22.4%, have an average optimal development. The level of scores for the rear width (5.9 score), attachment of the fore (6.3 score) and the rear parts (6.0 score) of the udder testifies to their good development. The body structure of the cows-firstborn has a sufficient description of the type traits that determine their milk yield. At the present stage of selection and breeding work due to the use of bull-sires different origins and breeding value on the local population livestock with significant genotype diversity, the degree of influence each of the hereditary factors in the overall variability of linear features has a scientific and practical significance. In our studies, the force of influence conditional bloodiness of the Holstein mother's breed in the overall fraction of variability of linear type traits within the exterior complexes and the overall assessment takes a significant percentage - from 24.9 to 31.5 with a high degree of reliability according to Fischer's criterion. Among the descriptive traits, the proportion of influence the conditional bloodiness of mother, which is confirmed by high statistical confidence, ranges from 14.4 to 19.8%, and refers to the traits important for breeding. The level of coefficients of influence the father's breeding value in the total phenotypic variability for some of the linear traits is high and reliable. First of all it concerns group traits of the exterior, the development of which is determined by the pedigree value of father by 37.1–41.8%, and the overall assessment of type – by 46.6%. The coefficients of influence father's breeding value in most of the descriptive traits have high reliability (P < 0,001). The coefficients of the force of influence father, depending on the heredity of Holstein for the linear traits of almost the same level as his pedigree value. Since in this case the organized factor is purebreed Holstein and crossbreed bulls-sires of domestic selection, the positive role of Holstein heredity in improving the exterior type of cows has been traced realistically. The necessity of linear breeding, as an effective method in the system of dairy cattle breeding, has been substantiated by reliable values of the coefficients of the force of influence of father's line on the linear traits of offspring (3.4–29.5%). Despite the significant variability of coefficients of the force of influence on the linear traits, most of them have a high level of reliability within the evaluated body parts important for selection. The effect of cows belonging to the maternal line on the development of features of the body structure is insignificant and unreliable (5.3–9.2%). In the process of breeding aimed at improving cows of dairy herd by the exterior type, the pedigree value of parents has been assessed according to the method of linear classification of their daughters and their belonging to perspective genealogical formations.


10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.


Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.


Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4833-4844 ◽  
Author(s):  
Eda Yuluklu ◽  
Yilmaz Simsek ◽  
Takao Komatsu

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.


Author(s):  
Dusa McDuff ◽  
Dietmar Salamon

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.


Author(s):  
Peter Mann

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.


1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.


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