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1
Content available On the derivative of a polynomial
Jain Vinay Kumar
Journal of Mathematics and Applications
|
2023
|
Vol. 46
5--13
EN
For an arbitrary polynomial P(z), let M(P,r) =max|z|=r|P(z)| and m(P,r)=min|z|=r|P(z)|, (r >0). For a polynomial p(z)=Pn [wzór] of degreen, having all its zeros in|z|≤k, (k≥1), with a zero of orders, (s≥0), at 0 and F0, F1, F2, Gn-s, F3, F4, Hn-s, Fn-s, B0, B1, En-1, B2, B3, Dn-1 and Bn-1, as in Theorem, we have obtained a refinement [wzór] of our old result (1997), there by obtaining a new refinement of known results [wzór].
2
Content available remote On the equivalence between weak BMO and the space of derivatives of the Zygmund class
Kwessi Eddy
Demonstratio Mathematica
|
2021
|
Vol. 54, nr 1
140--150
EN
In this paper, we will discuss the space of functions of weak bounded mean oscillation. In particular, we will show that this space is the dual space of the special atom space, whose dual space was already known to be the space of derivative of functions (in the sense of distribution) belonging to the Zygmund class of functions. We show, in particular, that this proves that the Hardy space H1 strictly contains the special atom space.
3
Content available An operational calculus model with the (m,n) - symmetric difference
Wysocki Hubert
Scientific Journal of Polish Naval Academy
|
2020
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R. 61 nr 4 (223)
67--82
EN
The paper determines a non-classical Bittner operational calculus model, in which the derivative is understood as an -symmetric difference . By considering an operation , the formulated model has been generalized.
PL
W pracy określono model dyskretny nieklasycznego rachunku operatorów Bittnera, w którym pochodna rozumiana jest jako różnica -symetryczna . Dokonano uogólnienia opracowanego modelu rozważając operację .
4
Content available Exponential sequence in the operational calculus model for the nth-order forward difference
Wysocki Hubert
Scientific Journal of Polish Naval Academy
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2019
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R. 60 nr 2 (217)
35--47
EN
In the paper, there has been determined an exponential element in the discrete model of the non-classical Bittner operational calculus for the nth-order forward difference.
PL
W artykule wyznaczono element wykładniczy w dyskretnym modelu nieklasycznego rachunku operatorów Bittnera dla różnicy progresywnej rzędu n.
5
Content available A generalization of difference models of the Bittner operational calculus
Wysocki Hubert
Scientific Journal of Polish Naval Academy
|
2019
|
R. 60 nr 4 (219)
41--52
EN
In the paper, there has been constructed a discrete model of the non-classical Bittner operational calculus with a derivative understood as the operation Sb{x(k)}:={x(k+n)-b(k)x(k)} , which is a generalization of the n-order forward difference. It has also been pointed out that there is a possibility to generalize operational calculus models with backward and central differences of higher orders.
PL
W artykule skonstruowano model dyskretny nieklasycznego rachunku operatorów Bittnera z pochodną rozumianą jako operacja Sb{x(k)}:={x(k+n)-b(k)x(k)}, która jest uogólnieniem różnicy progresywnej rzędu n. Wskazano również na możliwość uogólnienia modeli rachunku operatorów z różnicą wsteczną i różnicą centralną wyższych rzędów.
6
Content available An operational calculus model for the central difference and exponential-trigonometric and hyperbolic Fibonacci sequences
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2018
|
R. 59 nr 3 (214)
39--62
EN
In the paper, there has been constructed such a non-classical Bittner operational calculus model, in which the derivative is understood as a central difference Dn {x(k)}:={x(k+n)-x(k-n)}. The discussed model has been generalized by considering the operation Dn,b {x(k)} : = {x(k+n)-bx(k-n)}, where b€C\{0}. In the D1 -difference model exponential-trigonometric and hyperbolic Fibonacci sequences have been introduced.
PL
W artykule skonstruowano model nieklasycznego rachunku operatorów Bittnera, w którym pochodna rozumiana jest jako różnica centralna Dn {x(k)}:={x(k+n)-x(k-n)}. Dokonano uogólnienia opracowanego modelu, rozważając operację Dn,b {x(k)} : = {x(k+n)-bx(k-n)}, gdzie b€C\{0}. . W modelu z różnicą D1 wprowadzono wykładniczo-trygonometryczne i hiperboliczne ciągi Fibonacciego.
7
Content available Experimental evaluation of forward speed effect on maneuvering hydrodynamic derivatives of a planing hull
Kazerooni M. F., Seif M. S.
Zeszyty Naukowe Akademii Morskiej w Szczecinie
|
2017
|
nr 49 (121)
40--53
EN
The calculation of unknown hydrodynamic derivatives of the equations of motion is the first step to estimate ship maneuverability and dynamic stability. These derivatives can be obtained theoretically, experimentally and numerically. Despite the development of the oblique towing model test to measure the hydrodynamic derivatives of displacement ships, limited experimental results are available for hydrodynamic derivatives of high speed crafts and speed dependency of the hydrodynamic derivatives is not understood well. In this paper a systematic series of model tests is described to determine the effect of forward speed on hydrodynamic derivatives of a monohull planing craft and the variations of the hydrodynamic derivatives by forward speed are derived. According to the results, hydrodynamic derivatives of planing hull are dramatically changed by variations of forward speed. Moreover, it is not possible to introduce a constant hydrodynamic derivative in the all the ranges of drift angle. Thus, the method of known constant hydrodynamic derivatives is not applicable to the simulation of planing craft maneuvering and variable hydrodynamic derivatives should be applied.
8
Content available Jackson and Hahn difference models as discrete Bittner operational calculus representations
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2017
|
R. 58 nr 4 (211)
61--70
EN
In the paper, there have been constructed discrete models of the non-classical Bittner operational calculus that are related to the notions of Jackson and Hahn derivatives, both known from the quantum calculus. To achieve it, we have used the Bittner operational calculus representation for the forward difference.
PL
W artykule skonstruowano dyskretne modele nieklasycznego rachunku operatorów Bittnera związane z pojęciami pochodnej Jacksona i pochodnej Hahna znanymi z rachunku kwantowego. Do tego celu wykorzystano reprezentację rachunku operatorów Bittnera dla różnicy progresywnej.
9
Content available An operational calculus model for the nth — order forward difference
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2017
|
R. 58 nr 3 (210)
107--117
EN
In this paper, there has been constructed such a model of a non-classical Bittner operational calculus, in which the derivative is understood as a forward difference Δn {x(k)}: = {x(k + n) – x(k)}. Next, considering the operation Δn,b {x(k)}: = {x(k + n) – b x(k)}, the presented model has been generalized.
PL
W artykule skonstruowano model nieklasycznego rachunku operatorów Bittnera, w którym pochodna rozumiana jest jako różnica progresywna Δn {x(k)}: = {x(k + n) – x(k)}. Następnie dokonano uogólnienia opracowanego modelu, rozważając operację Δn,b {x(k)}: = {x(k + n) – b x(k)}.
10
Content available On the derivative of a polynomial with prescribed zeros
Jain V. K.
Journal of Mathematics and Applications
|
2017
|
Vol. 40
97--120
EN
For a polynomial [wzór] of degree n having all its zeros in │z│ ≤ K, K ≥1 it is known that max [wzór]. By assuming a possible zero of order m, 0 ≤ m ≤ n - 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.
11
Content available A discrete non-classical operational calculus model with the Horadam difference
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2016
|
R. 57 nr 2 (205)
93--103
EN
In this paper, there has been constructed such a model of the non-classical Bittner operational calculus, in which the derivative related to Horadam sequences is understood as a difference operation S{x(k)} : = {x(k + 2) – a x(k + 1) – b x(k)}.
PL
W artykule skonstruowano model nieklasycznego rachunku operatorów Bittnera, w którym pochodna związana z ciągami Horadama rozumiana jest jako operacja różnicowa S{x(k)} : = {x(k + 2) – a x(k + 1) – b x(k)}.
12
Content available The operational calculus model for the nth-order backward difference
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2015
|
R. 56 nr 3 (202)
75--88
EN
In this paper, there has been constructed such a model of the non-classical Bittner operational calculus, in which the derivative is understood as the backward difference ∇n{x(k)} := {x(k) – x(k – n)}. Next, the presented model has been generalized by considering the operation ∇n,b{x(k)} := {x(k) – b x(k – n)}, where b ∈ C \ {0}.
PL
W artykule skonstruowano model nieklasycznego rachunku operatorów Bittnera, w którym pochodna rozumiana jest jako różnica wsteczna ∇n{x(k)} := {x(k) – x(k – n)}. Następnie dokonano uogólnienia opracowanego modelu, rozważając operację ∇n,b{x(k)} := {x(k) – b x(k – n)} , gdzie b ∈ C \ {0}.
13
Content available Spira Mirabilis in the selected models of Bittner operational calculus
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2015
|
R. 56 nr 4 (203)
65--96
EN
Parametric descriptions of spirals being analogues of the logarithmic spiral are determined using the concept of the exponential element in the non-classical Bittner operational calculus and applying the chosen models of it.
PL
Korzystając z pojęcia elementu wykładniczego w nieklasycznym rachunku operatorów Bittnera oraz stosując wybrane modele tego rachunku, wyznaczono opisy parametryczne spiral będących odpowiednikami spirali logarytmicznej.
14
Content available Improper Interpretation of Dilatometric Data for Cooling Transformation in Steels
Pawłowski B., Bała P., Dziurka R.
Archives of Metallurgy and Materials
|
2014
|
Vol. 59, iss. 3
1159--1161
EN
Dilatometry is the most commonly method of producing CCT diagrams and analyzing phase transformations during cooling (as well as transformations during heating) and it permits the real-time monitoring of the extent of reaction in terms of dimensional changes due to phase transformation. All modern dilatometers are fitted with computerised systems which collect dimensional change signals versus temperature to plot a dilatometric curve and also to calculate and plot the derivative of the relative dimensional change with respect to temperature. Unfortunately, elaborated by dilatometers manufacturers software, in many cases could lead to wrong interpretation of phase transformations during cooling.
PL
Dylatometria jest najczęściej stosowana technika badawczą przy tworzeniu wykresów CTPc i analizie przemian fazowych podczas chłodzenia oraz nagrzewania. Umożliwia również śledzenie na bieżąco postępu przemiany dzięki rejestracji zmian wymiarów próbki w trakcie przemiany. Wszystkie współczesne dylatometry są wyposażone w systemy komputerowe sterowania i akwizycji danych pomiarowych umożliwiające obserwację dylatogramu w trakcie chłodzenia czy nagrzewania jak również obliczenie i narysowanie po zakończeniu eksperymentu wykresu różniczki (pierwszej pochodnej) w funkcji temperatury. Niestety, fabryczne oprogramowanie w wielu przypadkach może prowadzić do błędnej interpretacji zjawisk podczas przemian fazowych w trakcie chłodzenia.
15
Content available Model ruchu operatorów dla różnicy wstecznej przy podstawach a, b
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2013
|
R. 54 nr 1 (192)
109--120
PL
W pracy skonstruowano dyskretny model rachunku operatorów Bittnera, w którym pochodna rozumiana jest jako operacja różnicowa ▼a,bu(k)=a(k)u(k)–b(k)u(k–1). Stanowi on uogólnienie ▼-modelu z różnicą wsteczną ▼u(k)=u(k)–u(k–1).
EN
The paper presents a discrete model of Bittner’s operational calculus, in which the derivative is understood as a difference operation ▼a,bu(k)=a(k)u(k)–b(k)u(k–1). The model is a generalization of the ▼-model with the backward difference ▼u(k)=u(k)–u(k–1).
16
Content available remote The nabla difference model of the operational calculus
Wysocki H.
Demonstratio Mathematica
|
2013
|
Vol. 46, nr 2
315--326
EN
In the paper, there has been constructed the (...)-model of the Bittner operational calculus for the backward difference (…) in the space of two-sided sequences. A form of the Taylor’s formula has been derived. Applying the operation (...), the (...)-model has been generalized.
17
Content available Analysing experimental research data with the help of numerical derivative
Książkiewicz A.
Computer Applications in Electrical Engineering
|
2013
|
Vol. 11
304--309
EN
A lot of research data is generated during carrying out experiments like for example in case of oscilloscope records. In this huge amount of information a lot of it is irrelevant. Therefore finding the useful information can be difficult. The influence of closing a short- circuit current with an electromagnetic relay on its contacts was tested. During those tests a large amount of data, recorded by oscilloscope, was created. Only a small portion of this information was useful. The problem was to find specific information in all of the gathered data. This article presents the usage of scientific software designed to solve this issue. It also describes the usage of numerical derivate for finding a specific time range of collected waveforms.
18
Content available Uogólnione liczby Horadama i rachunek różnic wstecznych
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2011
|
R. 52 nr 1 (184)
91-102
PL
W artykule wprowadzono pojęcie dwustronnego ciągu liczb Horadama n-tego rzędu. Za pomocą dyskretnego modelu nieklasycznego rachunku operatorów Bittnera opartego na różnicy wstecznej wyprowadzono wzór na ogólny wyraz ciągu będący odpowiednikiem wzoru Bineta dla ciągu Fibonacciego.
EN
The paper introduces the notion of a two-sided sequence of n-order Horadam numbers. Using of the non-classical Bittner operational calculus discrete model based on the backward difference , the general term of has been derived. The term is a parallel of Binet's formula for the Fibonacci sequence.
19
Content available remote A Lower Bound of the Second-order Nonlinearities of Boolean Bent Functions
Garg M., Gangopadhyay S.
Fundamenta Informaticae
|
2011
|
Vol. 111, nr 4
413-422
EN
In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = [formula], where d1 and d2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a recent result of Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is shown in Section 3, by a direct computation, that for large values of n, the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao.
20
Content available Model nieklasycznego rachunku operatorów Bittnera dla różnicy wstecznej
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2010
|
R. 51 nr 2 (181)
37-48
PL
W pracy skonstruowano -model rachunku operatorów Bittnera dla różnicy wstecznej u (k) = u (k) - u (k-1) w przestrzeni ciągów dwustronnych, w którym wyprowadzono postać wzoru Taylora. Dokonano uogólnienia modelu, rozważając operację u (k) = u (k) - u (k-1).
EN
In this paper there is constructed the -model of the Bittner operational calculus for the backward difference u (k) = u (k) - u (k-1) in the space of two-sided sequences, in which a form of the Taylor’s formula is determined. Considering the operation of u (k) = u (k) - u (k-1) the -model is generalized.
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