positive function
Recently Published Documents


TOTAL DOCUMENTS

241
(FIVE YEARS 67)

H-INDEX

20
(FIVE YEARS 2)

Author(s):  
V. Rovenski ◽  
P. Walczak

We introduce and study certain deformation of Minkowski norms in [Formula: see text] determined by a set of [Formula: see text] linearly independent 1-forms and a smooth positive function of [Formula: see text] variables. In particular, the deformation of a Euclidean norm [Formula: see text] produces a Minkowski norm defined in our recent work; its indicatrix is a rotation hypersurface with a [Formula: see text]-dimensional axis passing through the origin. For [Formula: see text], our deformation generalizes the construction of [Formula: see text]-norms which form a rich class of “computable” Minkowski norms and play an important role in Finsler geometry. We characterize such pairs of a Minkowski norm and its image that Cartan torsions of the two norms either coincide or differ by a [Formula: see text]-reducible term. We conjecture that for [Formula: see text] any Minkowski norm can be approximated by images of a Euclidean norm.


2021 ◽  
Vol 13 (23) ◽  
pp. 13074
Author(s):  
Tao Zhang ◽  
Qinian Hu ◽  
Qi Ding ◽  
Dian Zhou ◽  
Weijun Gao ◽  
...  

In the context of the Chinese rural revitalization strategy, the unique residential characteristics of local vernacular dwellings formed by profound historical and cultural accumulation, climate characteristics, and residential lifestyle have undergone profound change in the gully regions of the Loess Plateau. Accordingly, the contradictions of traditional vernacular dwelling protection, increasing living requirements, and ecological protection have intensified. In this paper, with the aim of optimizing courtyard layout for vernacular dwellings, the thermal performance and regional adaptability of different courtyard layouts were analyzed using Ladybug and Honeybee tools. According to the thermal simulation within the courtyard, the current optimal layout type was determined, and then, several ecological optimization designs were proposed for the further improvement of it. The results revealed that the improved vernacular dwelling model has better regional adaptability, which corresponds to the local living culture and living habits, saves land resources, and provides a better thermal comfort performance. This research not only has a positive function for the protection of local architectural culture, but also plays an essential role in improving residents’ living comfort and living standards. We hope that the research results are meaningful and can be used as a reference for future rural construction in the Loess Plateau.


2021 ◽  
Vol 58 (4) ◽  
pp. 890-908
Author(s):  
Caio Alves ◽  
Rodrigo Ribeiro ◽  
Rémy Sanchis

AbstractWe prove concentration inequality results for geometric graph properties of an instance of the Cooper–Frieze [5] preferential attachment model with edge-steps. More precisely, we investigate a random graph model that at each time $t\in \mathbb{N}$ , with probability p adds a new vertex to the graph (a vertex-step occurs) or with probability $1-p$ an edge connecting two existent vertices is added (an edge-step occurs). We prove concentration results for the global clustering coefficient as well as the clique number. More formally, we prove that the global clustering, with high probability, decays as $t^{-\gamma(p)}$ for a positive function $\gamma$ of p, whereas the clique number of these graphs is, up to subpolynomially small factors, of order $t^{(1-p)/(2-p)}$ .


2021 ◽  
pp. 1-16
Author(s):  
Leigh G. Goetschius ◽  
Vonnie C. McLoyd ◽  
Tyler C. Hein ◽  
Colter Mitchell ◽  
Luke W. Hyde ◽  
...  

Abstract School connectedness, a construct indexing supportive school relationships, has been posited to promote resilience to environmental adversity. Consistent with prominent calls in the field, we examined the protective nature of school connectedness against two dimensions of early adversity that index multiple levels of environmental exposure (violence exposure, social deprivation) when predicting both positive and negative outcomes in longitudinal data from 3,246 youth in the Fragile Families and Child Wellbeing Study (48% female, 49% African American). Child and adolescent school connectedness were promotive, even when accounting for the detrimental effects of early adversity. Additionally, childhood school connectedness had a protective but reactive association with social deprivation, but not violence exposure, when predicting externalizing symptoms and positive function. Specifically, school connectedness was protective against the negative effects of social deprivation, but the effect diminished as social deprivation became more extreme. These results suggest that social relationships at school may compensate for low levels of social support in the home and neighborhood. Our results highlight the important role that the school environment can play for youth who have been exposed to adversity in other areas of their lives and suggest specific groups that may especially benefit from interventions that boost school connectedness.


2021 ◽  
Vol 12 ◽  
Author(s):  
Luca Caricati ◽  
Chuma Kevin Owuamalam ◽  
Chiara Bonetti

Do superordinate in-group bias as well as temporal and social comparisons offer standalone explanations for system justification? We addressed this question using the latest World Value Survey (7th Wave), combining the responses of 55,721 participants from 40 different nations. Results from a random slope multilevel model showed that superordinate (national) identification, temporal comparison (i.e., the outcomes of an individual relative to those of his/her parents at different time points), and social comparison (based on income levels) were independent and positive predictors of system justification. Specifically, system justification increased when national identification was high, when income increased (i.e., the socioeconomic comparison was positive), and when the outcomes of citizens improved relative to the outcomes of their parents at relevant time points (i.e., the temporal comparison was positive). Incidentally, we also observed an interaction between national identification and temporal comparison (but not with social comparison), indicating that positive temporal comparison seemed to have a reduced effect (but still significant) for highly identified citizens. These results are supportive of the social identity approach to system justification and suggest that support for societal systems is a positive function of people’s personal and group interests.


2021 ◽  
Vol 56 (1) ◽  
pp. 28-38
Author(s):  
A.O. Korenovskii

For a positive function $f$ on the interval $[0,1]$, the power mean of order $p\in\mathbb R$ is defined by \smallskip\centerline{$\displaystyle\|\, f\,\|_p=\left(\int_0^1 f^p(x)\,dx\right)^{1/p}\quad(p\ne0),\qquad\|\, f\,\|_0=\exp\left(\int_0^1\ln f(x)\,dx\right).$} Assume that $0<A<B$, $0<\theta<1$ and consider the step function$g_{A<B,\theta}=B\cdot\chi_{[0,\theta)}+A\cdot\chi_{[\theta,1]}$, where $\chi_E$ is the characteristic function of the set $E$. Let $-\infty<p<q<+\infty$. The main result of this work consists in finding the term \smallskip\centerline{$\displaystyleC_{p<q,A<B}=\max\limits_{0\le\theta\le1}\frac{\|\,g_{A<B,\theta}\,\|_q}{\|\,g_{A<B,\theta}\,\|_p}.$} \smallskip For fixed $p<q$, we study the behaviour of $C_{p<q,A<B}$ and $\theta_{p<q,A<B}$ with respect to $\beta=B/A\in(1,+\infty)$.The cases $p=0$ or $q=0$ are considered separately. The results of this work can be used in the study of the extremal properties of classes of functions, which satisfy the inverse H\"older inequality, e.g. the Muckenhoupt and Gehring ones. For functions from the Gurov-Reshetnyak classes, a similar problem has been investigated in~[4].


Author(s):  
Bartłomiej Przybylski

AbstractWe consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.


10.37236/9135 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Meng Liu ◽  
Yusheng Li

Let $f(n)$ be a positive function and $H$ a graph. Denote by $\textbf{RT}(n,H,f(n))$ the maximum number of edges of an $H$-free graph on $n$ vertices with independence number less than $f(n)$. It is shown that  $\textbf{RT}(n,K_4+mK_1,o(\sqrt{n\log n}))=o(n^2)$ for any fixed integer $m\geqslant 1$ and $\textbf{RT}(n,C_{2m+1},f(n))=O(f^2(n))$ for any fixed integer $m\geqslant 2$ as $n\to\infty$.


2021 ◽  
Author(s):  
Silvestru Sever Dragomir

For a continuous and positive function w(λ), λ > 0 and μ a positive measure on (0, ∞) we consider the followingmonotonic integral transformwhere the integral is assumed to exist forT a positive operator on a complex Hilbert spaceH. We show among others that, if β ≥ A, B ≥ α > 0, and 0 < δ ≤ (B − A)2 ≤ Δ for some constants α, β, δ, Δ, thenandwhere is the second derivative of as a real function.Applications for power function and logarithm are also provided.


2021 ◽  
Vol 11 (1) ◽  
pp. 417-431
Author(s):  
Jing Yang ◽  
Ting Zhou

Abstract We are concerned with the following Schrödinger system with coupled quadratic nonlinearity − ε 2 Δ v + P ( x ) v = μ v w , x ∈ R N , − ε 2 Δ w + Q ( x ) w = μ 2 v 2 + γ w 2 , x ∈ R N , v > 0 , w > 0 , v , w ∈ H 1 R N , $$\begin{equation}\left\{\begin{array}{ll}-\varepsilon^{2} \Delta v+P(x) v=\mu v w, & x \in \mathbb{R}^{N}, \\ -\varepsilon^{2} \Delta w+Q(x) w=\frac{\mu}{2} v^{2}+\gamma w^{2}, & x \in \mathbb{R}^{N}, \\ v>0, \quad w>0, & v, w \in H^{1}\left(\mathbb{R}^{N}\right),\end{array}\right. \end{equation}$$ which arises from second-harmonic generation in quadratic media. Here ε > 0 is a small parameter, 2 ≤ N < 6, μ > 0 and μ > γ, P(x), Q(x) are positive function potentials. By applying reduction method, we prove that if x 0 is a non-degenerate critical point of Δ(P + Q) on some closed N − 1 dimensional hypersurface, then the system above has a single peak solution (vε , wε ) concentrating at x 0 for ε small enough.


Sign in / Sign up

Export Citation Format

Share Document