scholarly journals Structure of the set of Borel exceptional vectors for entire curves. II

2021 ◽  
Vol 55 (2) ◽  
pp. 137-145
Author(s):  
A.I. Bandura ◽  
Ya.I. Savchuk
Keyword(s):  
Finite Union ◽  
Zero Order ◽  
Integer Order ◽  
Independent Components ◽  
Linearly Independent ◽  
Union Of Subspaces ◽  
Zero Vector ◽  
Common Zeros

We have obtained a description of structure of the sets of Picard and Borel exceptional vectors for transcendental entire curve in some sense. We consider only $p$-dimensional entire curves with linearly independent components without common zeros.In particular, the set of Borel exceptional vectors together with the zero vector is a finite union of subspaces in $\mathbb{C}^{p}$ of dimension at most $p-1$. Moreover, the sum of their dimensions does not exceed $p$ if anypairwise intersection of the subspaces contains only the zero vector. A similar result is also valid for the set of Picardexceptional vectors.Another result shows that the structure of the set of Borel exceptional vectors for an entire curve of integer orderdiffers somewhat from the structure of such a set for an entire curve of non-integer order.For a transcendental entire curve $\vec{G}:\mathbb{C}\to \mathbb{C}^{p}$ with linearly independent components and without common zeros having non-integer or zero order the set of Borel exceptional vectors together with the zero vector is a subspace in $\mathbb{C}^{p}$ of dimension at most $p-1$. However, the set of Picard exceptional vectors does not possess this property. We propose two examples of entire curves.The first example shows the set of Borel exceptional vectors together with the zero vector for $p$-dimensional entire curve of integer order isunion of subspaces of dimension at most $p-1$ such that the total sum of these dimensions does not exceed $p$ and intersection of any pair of these subspaces contains only zero vector. The set of Picard exceptional vectors for the curve has the same property.In the second example, we construct a $q$-dimensional entire curve of non-integer order for which the set of Borel exceptional vectors together with the zero vector is a subspace in $\mathbb{C}^{q}$ of dimension at most $q-1$ and the set of Picard exceptional vectors together with the zero vectordo not have the property. This set is a union of some subspaces.

scholarly journals Asymptotic vectors of entire curves

2021 ◽  
Vol 56 (1) ◽  
pp. 48-54
Author(s):  
Ya.I. Savchuk ◽  
A.I. Bandura
Keyword(s):  
Meromorphic Functions ◽  
Counting Function ◽  
Sufficient Conditions ◽  
Positive Order ◽  
Independent Components ◽  
Number Of Zeros ◽  
Linearly Independent ◽  
Exceptional Value ◽  
Zero Vector ◽  
Common Zeros

We introduce a concept of asymptotic vector of an entire curve with linearly independent components and without common zeros and investigate a relationship between the asymptotic vectors and the Picard exceptional vectors. A non-zero vector $\vec{a}=(a_1,a_2,\ldots,a_p)\in \mathbb{C}^{p}$ is called an asymptotic vector for the entire curve $\vec{G}(z)=(g_1(z),g_2(z),\ldots,g_p(z))$ if there exists a continuous curve $L: \mathbb{R}_+\to \mathbb{C}$ given by an equation $z=z\left(t\right)$, $0\le t<\infty $, $\left|z\left(t\right)\right|<\infty $, $z\left(t\right)\to \infty $ as $t\to \infty $ such that$$\lim\limits_{\stackrel{z\to\infty}{z\in L}} \frac{\vec{G}(z)\vec{a} }{\big\|\vec{G}(z)\big\|}=\lim\limits_{t\to\infty} \frac{\vec{G}(z(t))\vec{a} }{\big\|\vec{G}(z(t))\big\|} =0,$$ where $\big\|\vec{G}(z)\big\|=\big(|g_1(z)|^2+\ldots +|g_p(z)|^2\big)^{1/2}$, $\vec{G}(z)\vec{a}=g_1(z)\cdot\bar{a}_1+g_2(z)\cdot\bar{a}_2+\ldots+g_p(z)\cdot\bar{a}_p$. A non-zero vector $\vec{a}=(a_1,a_2,\ldots,a_p)\in \mathbb{C}^{p}$ is called a Picard exceptional vector of an entire curve $\vec{G}(z)$ if the function $\vec{G}(z)\vec{a}$ has a finite number of zeros in $\left\{\left|z\right|<\infty \right\}$. We prove that any Picard exceptional vector of transcendental entire curve with linearly independent com\-po\-nents and without common zeros is an asymptotic vector.Here we de\-mon\-stra\-te that the exceptional vectors in the sense of Borel or Nevanlina and, moreover, in the sense of Valiron do not have to be asymptotic. For this goal we use an example of meromorphic function of finite positive order, for which $\infty $ is no asymptotic value, but it is the Nevanlinna exceptional value. This function is constructed in known Goldberg and Ostrovskii's monograph``Value Distribution of Meromorphic Functions''.Other our result describes sufficient conditions providing that some vectors are asymptotic for transcendental entire curve of finite order with linearly independent components and without common zeros. In this result, we require that the order of the Nevanlinna counting function for this curve and for each such a vector is less than order of the curve.At the end of paper we formulate three unsolved problems concerning asymptotic vectors of entire curve.

Strain measurement in In0.2Ga0.8As/GaAs quantum wires by convergent beam electron diffraction

1995 ◽  
Vol 53 ◽  
pp. 444-445
Author(s):  
S. Hillyard ◽  
Y.-P. Chen ◽  
J.D. Reed ◽  
W.J. Schaff ◽  
L.F. Eastman ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Semiconductor Lasers ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Convergent Beam Electron Diffraction ◽  
Zero Order ◽  
Beam Electron ◽  
Local Lattice ◽  
Device Applications ◽  
Convergent Beam

The positions of high-order Laue zone (HOLZ) lines in the zero order disc of convergent beam electron diffraction (CBED) patterns are extremely sensitive to local lattice parameters. With proper care, these can be measured to a level of one part in 104 in nanometer sized areas. Recent upgrades to the Cornell UHV STEM have made energy filtered CBED possible with a slow scan CCD, and this technique has been applied to the measurement of strain in In0.2Ga0.8 As wires.Semiconductor quantum wire structures have attracted much interest for potential device applications. For example, semiconductor lasers with quantum wires should exhibit an improvement in performance over quantum well counterparts. Strained quantum wires are expected to have even better performance. However, not much is known about the true behavior of strain in actual structures, a parameter critical to their performance.

Study on Discrete Autonomous Traffic Flow Model with Zero-Order Hold

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Lidong Zhang ◽  
Wenxing Zhu ◽  
Mengmeng Zhang ◽  
Cuijiao Chen
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Zero Order ◽  
Traffic Flow Model

Productly linearly independent sequences

2015 ◽  
Vol 52 (3) ◽  
pp. 350-370
Author(s):  
Jaroslav Hančl ◽  
Katarína Korčeková ◽  
Lukáš Novotný
Keyword(s):  
Rational Numbers ◽  
Infinite Products ◽  
Linearly Independent ◽  
New Concepts ◽  
Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

Space creation, structural construction and force distribution

2013 ◽  
Vol 4 (1) ◽  
pp. 1-12
Author(s):  
G. Lámer
Keyword(s):  
The Other ◽  
Frame Structure ◽  
Force Distribution ◽  
Independent Components ◽  
Other Hand

Abstract The paper is an overview of issues related to the space creation of a building, possibilities of developing frame structure and connections of force distribution in the construction. In plane the force distribution can be compression, bending and tension. In space “enclosing” a geometric solid means space creation. In space as it is to be expected, the force distribution must be compression, bending and tension in two different directions at the same time. This can be really variant but in the case of surface or surface-like constructions generated by translations (and/or rotations) on one hand, there are some other surfaces, which cannot be generated by translations (and/or rotations), on the other hand, the dimension of the inside “forces” is not two but three (independent components of a two-by-two tensor either in the case of compression tension, or in the case of bending). By this, force distribution is more complicated in space than in plane.

A Multivariate Analysis of the Pathological Narcissism Inventory’s Nomological Network

2017 ◽  
Author(s):  
Elizabeth A. Edershile ◽  
Leonard Simms ◽  
Aidan G.C. Wright
Keyword(s):  
Multivariate Analysis ◽  
Zero Order ◽  
Hierarchical Regression ◽  
Nomological Network ◽  
Pathological Narcissism ◽  
Personality Variables ◽  
Unique Variance ◽  
Pathological Narcissism Inventory ◽  
Narcissistic Grandiosity

The Pathological Narcissism Inventory (PNI; Pincus et al., 2009) has enjoyed widespread use in the study of the narcissism. However, questions have been raised about whether the PNI’s grandiosity scale adequately captures narcissistic grandiosity as well as other popular measures do. Specifically, some have noted that PNI grandiosity shows a pattern of external associations that diverges from patterns for narcissistic grandiosity predicted by experts, and is more similar to the predictions for the vulnerability scale than is desirable. Previous research driving these critiques has relied on patterns of zero-order correlations to examine the nomological networks of these scales. The present study reexamines the nomological networks of PNI grandiosity and vulnerability scales using hierarchical regression. Results indicate that once accounting for overlapping variance of vulnerability and grandiosity, the unique variance in the PNI’s grandiosity scale closely matches contemporary expert conceptualizations of narcissistic grandiosity based on expected associations with other personality variables.

Formulation and Evaluation of Nelfinavir Extended Release Trilayer Matrix Tablets by Design of Experiment

2018 ◽  
Vol 11 (5) ◽  
pp. 4259-4268
Author(s):  
Nirmala Rangu ◽  
Gande Suresh
Keyword(s):  
Controlled Release ◽  
Drug Release ◽  
Hydroxypropyl Methylcellulose ◽  
Magnesium Stearate ◽  
Zero Order ◽  
Matrix Tablets ◽  
Drug Dissolution ◽  
Crystalline Cellulose ◽  
Dissolution Profile ◽  
Release Formulation

The present study was aimed to develop once-daily controlled release trilayer matrix tablets of nelfinavir to achieve zero-order drug release for sustained plasma concentration. Nelfinavir trilayer matrix tablets were prepared by direct compression method and consisted of middle active layer with different grades of hydroxypropyl methylcellulose (HPMC), PVP (Polyvinyl Pyrrolidine) K-30 and MCC (Micro Crystalline Cellulose). Barrier layers were prepared with Polyox WSR-303, Xanthan gum, microcrystalline cellulose and magnesium stearate. Based on the evaluation parameters, drug dissolution profile and release drug kinetics DF8 were found to be optimized formulation. The developed drug delivery system provided prolonged drug release rates over a period of 24 h. The release profile of the optimized formulation (DF8) was described by the zero-order and best fitted to Higuchi model. FT-IR studies confirmed that there were no chemical interactions between drug and excipients used in the formulation. These results indicate that the approach used could lead to a successful development of a controlled release formulation of nelfinavir in the management of AIDS.

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