scholarly journals Localization theorems for matrices and bounds for the zeros of polynomials over quaternion division algebra

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 553-573 ◽  
Author(s):  
Sk. Ahmad ◽  
Istkhar Ali
Keyword(s):  
Zeros Of Polynomials ◽  
Sufficient Condition ◽  
Complex Matrix ◽  
Quaternionic Matrix ◽  
Left And Right ◽  
The Stability ◽  
The Right ◽  
Left And Right Eigenvalues ◽  
Quaternionic Polynomials

In this paper, we derive Ostrowski and Brauer type theorems for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic matrix. After that, a sufficient condition for the stability of a quaternionic matrix is given that generalizes the stability condition for a complex matrix. Finally, a characterization of bounds is derived for the zeros of quaternionic polynomials.

scholarly journals Analysis of suspension bridge tunnel-type anchorage construction on the stability of surrounding rock

2020 ◽  
Vol 198 ◽  
pp. 02006
Author(s):  
Nana Li ◽  
Yongqiang Zhou ◽  
Yanqiang Zhao ◽  
Guiju Li
Keyword(s):  
Suspension Bridge ◽  
Surrounding Rock ◽  
Construction Process ◽  
Analysis Model ◽  
Stability Of Surrounding Rock ◽  
Numerical Software ◽  
Left And Right ◽  
Simulation Results ◽  
The Stability ◽  
The Right

In order to study the interaction between the left and right tunnels of suspension bridge tunnel-type anchorage, the finite difference numerical software is used to analyze the mechanical properties of the surrounding rock during the construction process. A numerical analysis model based on FLAC3D is established to analyze the stress, displacement and plastic zone changes of the surrounding rock of right tunnel anchor cavern during the construction of left tunnel anchor cavern. The right tunnel anchor cavern is excavated firstly, and then the left tunnel anchor cavern is excavated. The numerical simulation results show that the main displacement of the right tunnel occurs in the construction stage of the anchor plug body and the rear anchor cavern of the left tunnel. During the excavation of the left tunnel, the plastic zones of the left and right tunnel anchor caverns are only connected above the middle of the waist wall. Therefore, it is suggested that during the construction process, especially in the excavation stage of the anchor plug body and the rear anchor cavern, the area above the middle of the tunnel waist wall should be strengthened in time to ensure the construction safety.

scholarly journals Polynomial equations over octonion algebras

2019 ◽  
Vol 19 (06) ◽  
pp. 2050102 ◽  
Author(s):  
Adam Chapman
Keyword(s):  
Division Algebra ◽  
Conjugacy Classes ◽  
Companion Matrix ◽  
Polynomial Equations ◽  
Left And Right ◽  
The Right ◽  
Octonion Algebras ◽  
Left And Right Eigenvalues

In this paper, we present a complete method for finding the roots of all polynomials of the form [Formula: see text] over a given octonion division algebra. When [Formula: see text] is monic, we also consider the companion matrix and its left and right eigenvalues and study their relations to the roots of [Formula: see text], showing that the right eigenvalues form the conjugacy classes of the roots of [Formula: see text] and the left eigenvalues form a larger set than the roots of [Formula: see text].

scholarly journals Lateralization of face processing in the human brain

2012 ◽  
Vol 279 (1735) ◽  
pp. 2052-2061 ◽  
Author(s):  
Ming Meng ◽  
Tharian Cherian ◽  
Gaurav Singal ◽  
Pawan Sinha
Keyword(s):  
Face Processing ◽  
Inhibitory Influence ◽  
Hemispheric Differences ◽  
Response Dynamics ◽  
Activation Patterns ◽  
Face Selectivity ◽  
Left And Right ◽  
The Right ◽  
Processing Mechanisms

Are visual face processing mechanisms the same in the left and right cerebral hemispheres? The possibility of such ‘duplicated processing’ seems puzzling in terms of neural resource usage, and we currently lack a precise characterization of the lateral differences in face processing. To address this need, we have undertaken a three-pronged approach. Using functional magnetic resonance imaging, we assessed cortical sensitivity to facial semblance, the modulatory effects of context and temporal response dynamics. Results on all three fronts revealed systematic hemispheric differences. We found that: (i) activation patterns in the left fusiform gyrus correlate with image-level face-semblance, while those in the right correlate with categorical face/non-face judgements. (ii) Context exerts significant excitatory/inhibitory influence in the left, but has limited effect on the right. (iii) Face-selectivity persists in the right even after activity on the left has returned to baseline. These results provide important clues regarding the functional architecture of face processing, suggesting that the left hemisphere is involved in processing ‘low-level’ face semblance, and perhaps is a precursor to categorical ‘deep’ analyses on the right.

Sequent-systems for modal logic

1985 ◽  
Vol 50 (1) ◽  
pp. 149-168 ◽  
Author(s):  
Kosta Došen
Keyword(s):  
Order Logic ◽  
Philosophical Logic ◽  
Logical Constants ◽  
First Order ◽  
Sequent Systems ◽  
Left And Right ◽  
Level 1 ◽  
The Right ◽  
Level 2

AbstractThe purpose of this work is to present Gentzen-style formulations of S5 and S4 based on sequents of higher levels. Sequents of level 1 are like ordinary sequents, sequents of level 2 have collections of sequents of level 1 on the left and right of the turnstile, etc. Rules for modal constants involve sequents of level 2, whereas rules for customary logical constants of first-order logic with identity involve only sequents of level 1. A restriction on Thinning on the right of level 2, which when applied to Thinning on the right of level 1 produces intuitionistic out of classical logic (without changing anything else), produces S4 out of S5 (without changing anything else).This characterization of modal constants with sequents of level 2 is unique in the following sense. If constants which differ only graphically are given a formally identical characterization, they can be shown inter-replaceable (not only uniformly) with the original constants salva provability. Customary characterizations of modal constants with sequents of level 1, as well as characterizations in Hilbert-style axiomatizations, are not unique in this sense. This parallels the case with implication, which is not uniquely characterized in Hilbert-style axiomatizations, but can be uniquely characterized with sequents of level 1.These results bear upon theories of philosophical logic which attempt to characterize logical constants syntactically. They also provide an illustration of how alternative logics differ only in their structural rules, whereas their rules for logical constants are identical.

scholarly journals Multivaluedness in Networks: Theory

2020 ◽  
Author(s):  
Anton van Wyk
Keyword(s):  
Structural Complexity ◽  
The Other ◽  
Sufficient Condition ◽  
The Novel ◽  
Necessary And Sufficient Condition ◽  
Cascaded Systems ◽  
The Right ◽  
Necessary And Sufficient ◽  
Theoretical Results

<div>An unexpected and somewhat surprising observation is that two counter-cascaded systems,12 satisfying the right conditions, implicitly exhibit multivaluedness from one of the outputs to the other. Based on the novel notions of immanence and transcendence, the main result presented here, gives a necessary and sufficient condition for multivaluedness to be exhibited by counter-cascaded systems. Subsequent corollaries provide further characterization of multivaluedness under specific conditions.</div><div><br></div><div>As an application of these theoretical results, we demonstrate how these aid in the structural complexity reduction of directed complex networks.</div>

scholarly journals Genetic analysis of the heterochromatin of chromosome 3 in Drosophila melanogaster. I. Products of compound-autosome detachment.

Genetics ◽  
1988 ◽  
Vol 120 (2) ◽  
pp. 503-517
Author(s):  
G E Marchant ◽  
D G Holm
Keyword(s):  
Drosophila Melanogaster ◽  
Genetic Analysis ◽  
Genetic Characterization ◽  
Complementation Analysis ◽  
Chromosome 3 ◽  
Recessive Lethal ◽  
The Third ◽  
Left And Right ◽  
The Right

Abstract The heterochromatin of the third chromosome is the largest uncharacterized region of the Drosophila melanogaster genome, and the last major block of D. melanogaster heterochromatin to be thoroughly analyzed. In the present study, this region was genetically dissected by generating and analyzing a series of attached, detached and reattached third chromosomes. Separate detachment experiments were conducted for all 12 possible combinations of four newly synthesized sister-strand compound-3L and three newly synthesized sister-strand compound-3R chromosomes. A total of 443 recessive lethal detachment products carrying putative heterochromatic deficiencies were tested for complementation in a several-stage complementation analysis. The results revealed the presence of seven separable vital regions in the heterochromatin of chromosome 3. Attempts to reattach deficiency-carrying detachment products established that six of these vital regions are on the left arm, but only one is on the right arm. An analysis of the types and frequencies of detachment-product deficiencies generated in each detachment experiment permitted the genetic characterization of the progenitor compounds. It was also possible to determine the proximal-distal orientation of the genes on each arm, and to identify possible breakpoints for each lethal detachment product produced. The results of this study suggest that vital genes in the heterochromatin of the third chromosome are not randomly distributed between, nor within, the heterochromatic blocks of the left and right arms.

scholarly journals Further results on Left and Right Generalized Drazin Invertible Operators

2020 ◽  
Vol 54 (1) ◽  
pp. 98-106
Author(s):  
So. Messirdi ◽  
Sa. Messirdi ◽  
B. Messirdi
Keyword(s):  
Banach Space ◽  
Explicit Formula ◽  
Sufficient Conditions ◽  
Bounded Operators ◽  
Left And Right ◽  
The Right ◽  
Generalized Drazin Invertible Operators ◽  
Jacobson’S Lemma

In this paper we present some new characteristics and expressions of left and right generalized Drazin invertible bounded operators on a Banach space $X.$ An explicit formula relating the left and the right generalized Drazin inverses to spectral idempotents is provided. In addition, we give a characterization of operators in $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$) with equal spectral idempotents, where $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$) denotes the set of all left (resp. right) generalized Drazin invertible bounded operators on $X.$ Next, we give some sufficient conditions which ensure that the product of elements of $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$) remains in $\mathcal{B}_{l}(X)$ (resp. $\mathcal{B}_{r}(X)$). Finally, we extend Jacobson's lemma for left and right generalized Drazin invertibility. The provided results extend certain earlier works given in the literature.

scholarly journals Characterization of the 450-kb Linear Plasmid in a Polychlorinated Biphenyl Degrader, Rhodococcus sp. Strain RHA1

2001 ◽  
Vol 67 (5) ◽  
pp. 2021-2028 ◽  
Author(s):  
Satoru Shimizu ◽  
Hiroyuki Kobayashi ◽  
Eiji Masai ◽  
Masao Fukuda
Keyword(s):  
Southern Hybridization ◽  
Polychlorinated Biphenyl ◽  
Physical Map ◽  
Linear Plasmid ◽  
Southern Hybridization Analysis ◽  
Gel Shift Assay ◽  
Left And Right ◽  
The Right ◽  
Degradative Enzyme

ABSTRACT A strong polychlorinated biphenyl (PCB) degrader,Rhodococcus sp. strain RHA1, has diverse biphenyl/PCB degradative genes and harbors huge linear plasmids, including pRHL1 (1,100 kb), pRHL2 (450 kb), and pRHL3 (330 kb). The diverse degradative genes are distributed mainly on the pRHL1 and pRHL2 plasmids. In this study, the structural and functional characteristics of pRHL2 were determined. We constructed a physical map of pRHL2, and the degradative enzyme genes, including bphB2, etbD2, etbC, bphDEF, bphC2, and bphC4, were localized in three regions. Conjugal transfer of pRHL2 between RHA1 mutant derivatives was observed at a frequency of 7.5 × 10−5 transconjugant per recipient. These results suggested that the linear plasmid is a possible determinant of propagation of the diverse degradative genes in rhodococci. The termini of pRHL2 were cloned and sequenced. The left and right termini of pRHL2 had 3-bp perfect terminal inverted repeats and were not as similar to each other (64% identity) as the known actinomycete linear replicons are. Southern hybridization analysis with pRHL2 terminal probes suggested that the right terminus of pRHL2 is similar to pRHL1 and pRHL3 termini. Retardation of both terminal fragments in the gel shift assay indicated that each terminus of pRHL2 is linked to a protein. We suggest that pRHL2 has invertron termini, as has been reported previously for Streptomyces linear replicons.

TEM characterization of Au/Polysilicon interactions

1990 ◽  
Vol 48 (4) ◽  
pp. 650-651
Author(s):  
N. David Theodore ◽  
Leslie H. Allen ◽  
C. Barry Carter ◽  
James W. Mayer
Keyword(s):  
Solid Phase ◽  
Single Crystal Silicon ◽  
Chemical Vapor ◽  
Electrical Contacts ◽  
Silicon Substrates ◽  
Crystal Silicon ◽  
Transmission Electron ◽  
Polysilicon Films ◽  
The Stability

Metal/polysilicon investigations contribute to an understanding of issues relevant to the stability of electrical contacts in semiconductor devices. These investigations also contribute to an understanding of Si lateral solid-phase epitactic growth. Metals such as Au, Al and Ag form eutectics with Si. reactions in these metal/polysilicon systems lead to the formation of large-grain silicon. Of these systems, the Al/polysilicon system has been most extensively studied. In this study, the behavior upon thermal annealing of Au/polysilicon bilayers is investigated using cross-section transmission electron microscopy (XTEM). The unique feature of this system is that silicon grain-growth occurs at particularly low temperatures ∽300°C).Gold/polysilicon bilayers were fabricated on thermally oxidized single-crystal silicon substrates. Lowpressure chemical vapor deposition (LPCVD) at 620°C was used to obtain 100 to 400 nm polysilicon films. The surface of the polysilicon was cleaned with a buffered hydrofluoric acid solution. Gold was then thermally evaporated onto the samples.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

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