Norms of Dual Complex Vectors and Dual Complex Matrices

In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

Norms in the Translation of Chinese Film Titles

A film title is an essential part of a film.Compared with the translation of book titles and news headings,film title translation has been received far less attention,especially the rendering of Chinese film titles into English versions.Therefore,the thesis aims to study Chinese film title translation in the framework of norm theory and investigate the strategies adopted by translators.

分配的完备格上的T-Norms的求解算法

智能控制已经从二元论发展到四元论,目前智能推理算法存在缺陷,寻求最优模糊控制系统的有效方法还没有真正给出。文中介绍了智能蕴含算子的概念及4种基本的T-Norms,给出了分配的完备格上的T-Norms关系式的求解算法以及与T(r)相伴的智能蕴含算子相关的计算公式,其作用是提升PID的建模思想,实现调节r,改良推理模型,完成最优控制。

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

On the Norms of r-Toeplitz Matrices Involving Fibonacci and Lucas Numbers

Let us define to be a r-Toeplitz matrix. The entries in the first row of are or;where Fn and Ln denote the usual Fibonacci and Lucas numbers, respectively. We obtained some bounds for the spectral norm of these matrices.

Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms

We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.

Negative Norms in Quantized Strings as Dark Energy Density of the Cosmos

The present short paper is concerned with accurate explanation as well as quantification of the so called missing dark energy of the cosmos. It was always one of the main objectives of any successful general theory of high energy particle physics and quantum cosmology to keep non-physical negative norms, the so called ghosts completely out of that theory. The present work takes the completely contrary view by admitting these supposedly spurious states as part of the physical Hilbert space. It is further shown that rethinking the ghost free condition with the two critical spacetime dimensions D1 = 26 and D2 = 25 together with the corresponding intercept a1 = 1 and a2 ≤ 1 respectively and in addition imposing, as in Gross et al. heterotic superstrings, an overall 496 dimensional exceptional Lie symmetry group, then one will discover that there are two distinct types of energy. The first is positive norm ordinary energy connected to the zero set quantum particles which is very close to the measured ordinary energy density of the cosmos, namely E(O) = mc2/22. The second is negative norm (i.e. ghost) energy connected to the empty set quantum wave and is equal to the conjectured dark energy density of the cosmos E(D) = mc2 (21/22) presumed to be behind the observed accelerated cosmic expansion. That way we were able to not only explain the physics of dark energy without adding any new concepts or novel additional ingredients but also we were able to compute the dark energy density accurately and in full agreement with measurements and observations.

The Review of Descriptive Norms in Translation Studies

The studies on descriptive norms in translation studies are of great significance because they spread the domain of norms and begin to consider the impact of the outside community so that they lead the study to a new field.Descriptive norms are discussed and studied systemically mainly by three scholars:Toury,Hermans,and Chesterman.The purpose of this article is to review this concept and try to point out some merits and demerits of their theory.

The Equivalence of Certain Norms on the Heisenberg Group

Let IHn be the (2n+1)-dimensional Heisenberg group. In this paper, we shall give among other things, the properties of some homogeneous norms relative to dilations on the IHn and prove the equivalence of these norms.

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with the property that its pushforward by the thinness function is a probability measure of truncated normal distribution. Finally, we improve this method to find a measure satisfying some important properties in geometric measure theory.

Misperceptions of peer gambling norms among adolescents: Analysis of a national sample in Finland

Introduction: Misperceptions of peer drinking norms are widely documented in the US student populations and are associated with increased personal consumption. Few studies have examined misperceptions of peer gambling, and none of these have been conducted among adolescents in the European context. In a national sample, we examined misperceptions of peer gambling in Finland. Tenets of the social norms approach form a framework for discussion of the findings. Methods: Participants were 4526 adolescents aged 12 to 18 years who completed the nationwide Adolescent Health and Lifestyle Survey in 2011. Main measures were gambling behavior and the perception of same age-sex peers’ gambling. Misperception was an overestimation of the frequency of gambling by others compared to the actual frequency of gambling. Results: Adolescents held substantial misperceptions of peer gambling, imagining they gambled much more than they actually did. Age, sex, and gambling behavior were correlated with the perceptions. The extent of misperception was greatest among monthly gamblers, whereas non-gamblers and daily gamblers were more accurate in their perceptions. Estimations of peers’ gambling frequency were more accurate in boys than in girls and among those aged 12 years than among older adolescents. Conclusion: Our findings suggest that adolescent gambling prevention efforts could benefit from adopting a social norms approach;that is, correcting gambling-related misperceptions might discourage gambling and protect adolescents from adopting more severe gambling patterns.

Cephalometric norms for a sample of Emirates adults

Introduction—European-American norms are still used in the orthodontic treatment of Emirates patients despite the different ethnic backgrounds of the Emirates. The purpose of this study was to formulate cephalometric norms for lateral cephalometric mea-surements of Emirates adults and to study gender differences. Methods—Lateral cephalometric radio-graphs of 176 Emirates adults, 91 males and 85 fe-males, were selected according to the following crite-ria;an age range between 19 to 25 years, esthetically pleasing and harmonious faces with balanced and acceptable profiles and occlusions, normal skeletal and dental relationship, all permanent teeth present, and no history of orthodontic treatment or facial trauma. The mean values and standard deviations of 91 angular and 21 linear cephalometric variables were calculated using the Dolphin version 10.5 soft-ware package. The resulting norms for Emirates male and female groups were compared using a student t-test. Results—Several statistically significant gender differences were noticeable. Skeletally, Emirates males showed significantly greater (p < 0.001) total, anterior, and posterior cranial base lengths as well as longer facial heights, greater SGn-FH (°), ANS Xi PM (°),and FH/MP (°) angles than females. In addition, Emirates males had significantly greater (p < 0.001) Co-A (mm), Co-Gn (mm), and significantly greater (p < 0.05) Pog-N vert (mm) than females. Dentally, Emirates males had significantly greater (p < 0.05) UI-SN (°) and U1-NA (°), U1-NA (mm), and L1-NB (mm) (p < 0.001) than females. For soft tissue measurements there were significant gender differences (p < 0.001) for all angular and linear measurements except for lower lip to E-plane and nose prominence measurements which have no significant gender difference. Emirates males revealed greater measurements than females except for soft tissue con-vexity, Z-angle, and both upper and lower lips pro-trusion which were significantly greater in Emirates females. Conclusions—The use of specific cephalometric standards for Emirates adults, sep-arate for gender, seems to be justified. It is appropri-ate to put these cephalometric norms into daily or-thodontic practice when Emirates adults are being treated.

Locating Multiple Facilities in Convex Sets with Fuzzy Data and Block Norms

In this paper we study the problem of locating multiple facilities in convex sets with fuzzy parameters. This problem asks to find the location of new facilities in the given convex sets such that the sum of weighted distances between new facilities and existing facilities is minimized. We present a linear programming model for this problem with block norms, then we use it for problems with fuzzy data. We also do this for rectilinear and infinity norms as special cases of block norms.

Protocol for a Respondent-Driven Sampling Study Exploring the Roles of Peer Norms in HIV-Related Practices of Gay Men

Introduction: Sexual behaviour among gay and other men who have sex with men (GMSM) is influenced by the shared understanding of HIV/STI risk and peer norms regarding sexual behaviour. However, there is little research evidence to support this relationship. The unique geographic spread of Australian communities, the history of Australian HIV epidemic and the different patterns in risky sexual practices and HIV diagnoses across Australia present an opportunity to explore the role of social norms and GMSM behaviours in shaping different patterns of HIV epidemics. We describe the protocol of the study of contemporary norms in networks and communities of GMSM (CONNECT) which investigates gay community behavioural norms and practices. Methods: CONNECT is aimed to 1) identify the patterns of connections between individuals in GMSM communities and assess how they shape HIV-related behaviours;2) describe the relationship between social norms and sexual practices;and 3) compare the norms and patterns of behaviour in geographically and epidemiologically distinct GMSM populations in three Australian states New South Wales, Victoria and Western Australia, in order to identify local community norms and barriers to effective HIV prevention. This quantitative cross-sectional study uses respondent-driven sampling (RDS) for recruitment. Results: Analyses will be carried out on individual and community level and will investigate the relationship between community-level behavioural norms and associated practices of individuals. Conclusion: CONNECT is anticipated to inform HIV prevention services to better target and increase the effectiveness of the current health promotion for GMSM in the context of increasing HIV/STI incidence.

Preceding Crops Selection, Colza Seeding Norms and Dates Optimization in North Kazakhstan

Colza is a relatively new crop for North Kazakhstan. The increase of colza seeds production is restricted by its cultivation technology imperfection. Empiric model of colza for seeds cultivation is designed, allowing using its maximum potential. It was found out that correct preceding crops selection, optimization of norms and dates of colza seeding provide seeds heavy weight crops, reducing crops production cost and increasing cost efficiency at 62% average.

New Constructions of Nullnorms on Bounded Lattices

We propose two more general methods to construct nullnorms on bounded lattices. By some illustrative examples, we demonstrate that the new method differ from the existing approaches.

On Maps Preserving Unitarily Invariant Norms of the Spectral Geometric Mean

We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between C*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.

Age norms for grating acuity and contrast sensitivity measured by Lea tests in the first three years of life

AIM： To determine age norms in the first three years of life for grating visual acuity and contrast sensitivity obtained with Lea grating test and Hiding Heidi low contrast face test. METHODS： Lea grating test was used to estimate binocular grating acuity and Hiding Heidi low contrast face test was used to estimate contrast sensitivity in 600 healthy infants and children. Age ranged from 3 to 36 mo subdivided into 12 groups subjected for full ophthalmologic and pediatric examinations.RESULTS： The grating acuity developed along the first three years of life. It ranged from 1.88±0.32 c/d at 3mo to 30.95±0.77 c/d at 36 mo. The most rapid development was during the first 12 mo and the slowest development was from 30 to 36 mo. The contrast sensitivity showed rapid development in the first two years of life. Its mean value ranged from 4.23±1.17 at 3mo to 78.26±8.21 at 24 mo. It was constant at the highest score（80） thereafter.CONCLUSION： Age norms for grating acuity along with contrast sensitivity offer a more comprehensive measure of spatial vision and should be incorporated in clinical practice for better visual assessment in preverbal and nonverbal children.