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Let [a,b]⊆R\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$[a,b]\subseteq \mathbb {R}$$\end{document} be a non-empty and non singleton closed interval and P={a=x0<⋯r-bounded variation, if the expression ∑i=1n|f(xi)-f(xi-1)|r\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\sum \nolimits ^{n}_{i=1}|f(x_i)-f(x_{i-1})|^{r}$$\end{document} is bounded for all possible partitions like P. One of the main results of the paper deals with the generalization of the classical Jordan decomposition theorem. We establish that for r∈]0,1]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r\in ]0,1]$$\end{document}, a function of r-bounded variation can be written as the difference of two monotone functions. While for r>1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r>1$$\end{document}, under minimal assumptions such a function can be treated as an approximately monotone function which can be closely approximated by a nondecreasing majorant. We also prove that for 0d-periodically increasing f(x)≤f(y)forallx,y∈Iwithy-x≥d.\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f(x)\le f(y)\quad \text{ for } \text{ all }\quad x,y\in I\quad \text{ with }\quad y-x\ge d.$$\end{document}We establish that in a compact interval any function satisfying d-bounded variation can be decomposed as the difference of a monotone and a d-periodically increasing function. The core details related to past results, motivation, structure of each and every section are thoroughly discussed below. [ABSTRACT FROM AUTHOR]

We extend known results on chordal graphs and distance-hereditary graphs to much larger graph classes by using only a common metric property of these graphs. Specifically, a graph is called αi\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _i$$\end{document}-metric (i∈N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$i\in {\mathcal {N}}$$\end{document}) if it satisfies the following αi\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _i$$\end{document}-metric property for every vertices u, w, v and x: if a shortest path between u and w and a shortest path between x and v share a terminal edge vw, then d(u,x)≥d(u,v)+d(v,x)-i\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d(u,x)\ge d(u,v) + d(v,x)-i$$\end{document}. Roughly, gluing together any two shortest paths along a common terminal edge may not necessarily result in a shortest path but yields a “near-shortest” path with defect at most i. It is known that α0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _0$$\end{document}-metric graphs are exactly ptolemaic graphs, and that chordal graphs and distance-hereditary graphs are αi\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _i$$\end{document}-metric for i=1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$i=1$$\end{document} and i=2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$i=2$$\end{document}, respectively. We show that an additive O(i)-approximation of the radius, of the diameter, and in fact of all vertex eccentricities of an αi\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _i$$\end{document}-metric graph can be computed in total linear time. Our strongest results are obtained for α1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _1$$\end{document}-metric graphs, for which we prove that a central vertex can be computed in subquadratic time, and even better in linear time for so-called (α1,Δ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\alpha _1,\varDelta )$$\end{document}-metric graphs (a superclass of chordal graphs and of plane triangulations with inner vertices of degree at least 7). The latter answers a question raised in Dragan (Inf Probl Lett 154:105873, 2020), 2020). Our algorithms follow from new results on centers and metric intervals of αi\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _i$$\end{document}-metric graphs. In particular, we prove that the diameter of the center is at most 3i+2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$3i+2$$\end{document} (at most 3, if i=1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$i=1$$\end{document}). The latter partly answers a question raised in Yushmanov and Chepoi (Math Probl Cybernet 3:217–232, 1991). [ABSTRACT FROM AUTHOR]

A covering problem is an integer linear program of type $$\min \{c^Tx\mid Ax\ge D,\ 0\le x\le d,\ x \in \mathbb {Z}\}$$ where $$A\in \mathbb {Z}^{m\times n}_+$$ , $$D\in \mathbb {Z}_+^m$$ , and $$c,d\in \mathbb {Z}_+^n$$ . In this paper, we study covering problems with additional precedence constraints $$\{x_i\le x_j \ \forall j\preceq i \in \mathcal {P}\}$$ , where $$\mathcal {P}=([n], \preceq )$$ is some arbitrary, but fixed partial order on the items represented by the column-indices of A. Such precedence constrained covering problems ( PCCPs) are of high theoretical and practical importance even in the special case of the precedence constrained knapsack problem, that is, where $$m=1$$ and $$d\equiv 1$$ . Our main result is a strongly-polynomial primal-dual approximation algorithm for PCCP with $$d\equiv 1$$ . Our approach generalizes the well-known knapsack cover inequalities to obtain an IP formulation which renders any explicit precedence constraints redundant. The approximation ratio of this algorithm is upper bounded by the width of $$\mathcal {P}$$ , that is, by the size of a maximum antichain in $$\mathcal {P}$$ . Interestingly, this bound is independent of the number of constraints. We are not aware of any other results on approximation algorithms for PCCP on arbitrary posets $$\mathcal {P}$$ . For the general case with $$d\not \equiv 1$$ , we present pseudo-polynomial algorithms. Finally, we show that the problem does not admit a PTAS under standard complexity assumptions. [ABSTRACT FROM AUTHOR]

For a degree sequence $$d:d_1\ge \cdots \ge d_n$$ , we consider the smallest chromatic number $$\chi _{\min }(d)$$ and the largest chromatic number $$\chi _{\max }(d)$$ among all graphs with degree sequence d. We show that if $$d_n\ge 1$$ , then $$\chi _{\min }(d)\le \max \left\{ 3,d_1-\frac{n+1}{4d_1}+4\right\} $$ , and, if $$\sqrt{n+\frac{1}{4}}-\frac{1}{2}>d_1\ge d_n\ge 1$$ , then $$\chi _{\max }(d)=\max \nolimits _{i\in [n]}\min \left\{ i,d_i+1\right\} $$ . For a given degree sequence d with bounded entries, we show that $$\chi _{\min }(d), \chi _{\max }(d)$$ , and also the smallest independence number $$\alpha _{\min }(d)$$ among all graphs with degree sequence d, can be determined in polynomial time. [ABSTRACT FROM AUTHOR]

Let $${{\mathbb{R}}}$$ and Y be the set of real numbers and a Banach space respectively, and $${f, g :{\mathbb{R}} \to Y}$$ . We prove the Ulam-Hyers stability theorems for the Pexider-quadratic functional equation $${f(x + y) + f(x - y) = 2f(x) + 2g(y)}$$ and the Drygas functional equation $${f(x + y) + f(x - y) = 2f(x) + f(y) + f(-y)}$$ in the restricted domains of form $${\Gamma_d := \Gamma \cap \{(x, y) \in {\mathbb{R}}^2 : |x| + |y| \ge d\}}$$ , where $${\Gamma}$$ is a rotation of $${B \times B \subset {\mathbb{R}}^2}$$ and $${B^c}$$ is of the first category. As a consequence we obtain asymptotic behaviors of the equations in a set $${\Gamma_d \subset {\mathbb{R}}^2}$$ of Lebesgue measure zero. [ABSTRACT FROM AUTHOR]

Given integers $$n \ge k >l \ge 1$$ and a $$k$$ -graph $$F$$ with $$|V(F)|$$ divisible by $$n$$ , define $$t_l^k(n,F)$$ to be the smallest integer $$d$$ such that every $$k$$ -graph $$H$$ of order $$n$$ with minimum $$l$$ -degree $$\delta _l(H) \ge d $$ contains an $$F$$ -factor. A classical theorem of Hajnal and Szemerédi in (Proof of a Conjecture of P. Erdős, pp. 601-623, ) implies that $$t^2_1(n,K_t) = (1-1/t)n$$ for integers $$t$$ . For $$k \ge 3$$ , $$t^k_{k-1}(n,K_k^k)$$ (the $$\delta _{k-1}(H)$$ threshold for perfect matchings) has been determined by Kühn and Osthus in (J Graph Theory 51(4):269-280, ) (asymptotically) and Rödl et al. in (J Combin Theory Ser A 116(3):613-636, ) (exactly) for large $$n$$ . In this paper, we generalise the absorption technique of Rödl et al. in (J Combin Theory Ser A 116(3):613-636, ) to $$F$$ -factors. We determine the asymptotic values of $$t^k_1(n,K_k^k(m))$$ for $$k = 3,4$$ and $$m \ge 1$$ . In addition, we show that for $$t>k = 3$$ and $$\gamma >0, t^3_{2}(n,K_t^3) \le ( 1- \frac{2}{t^2-3t+4} + \gamma ) n$$ provided $$n$$ is large and $$t | n$$ . We also bound $$t^3_{2}(n,K_t^3)$$ from below. In particular, we deduce that $$t^3_2(n,K_4^3) = (3/4+o(1))n$$ answering a question of Pikhurko in (Graphs Combin 24(4):391-404, ). In addition, we prove that $$t^k_{k-1}(n,K_t^k) \le (1- \left( {\begin{array}{c}t-1\\ k-1\end{array}}\right) ^{-1} + \gamma )n$$ for $$\gamma >0, k \ge 6$$ and $$t \ge (3+ \sqrt{5})k/2$$ provided $$n$$ is large and $$t | n$$ . [ABSTRACT FROM AUTHOR]

Given $$S= \{v_1, \dots , v_n\} \subset {\mathbb {R}}^m$$ and $$p \in {\mathbb {R}}^m$$ , testing if $$p \in conv(S)$$ , the convex hull of $$S$$ , is a fundamental problem in computational geometry and linear programming. First, we prove a Euclidean distance duality, distinct from classical separation theorems such as Farkas Lemma: $$p$$ lies in $$conv(S)$$ if and only if for each $$p' \in conv(S)$$ there exists a pivot, $$v_j \in S$$ satisfying $$d(p',v_j) \ge d(p,v_j)$$ . Equivalently, $$p \not \in conv(S)$$ if and only if there exists a witness, $$p' \in conv(S)$$ whose Voronoi cell relative to $$p$$ contains $$S$$ . A witness separates $$p$$ from $$conv(S)$$ and approximate $$d(p, conv(S))$$ to within a factor of two. Next, we describe the Triangle Algorithm: given $$\epsilon \in (0,1)$$ , an iterate, $$p' \in conv(S)$$ , and $$v \in S$$ , if $$d(p, p') < \epsilon d(p,v)$$ , it stops. Otherwise, if there exists a pivot $$v_j$$ , it replace $$v$$ with $$v_j$$ and $$p'$$ with the projection of $$p$$ onto the line $$p'v_j$$ . Repeating this process, the algorithm terminates in $$O(mn \min \{ \epsilon ^{-2}, c^{-1}\ln \epsilon ^{-1} \})$$ arithmetic operations, where $$c$$ is the visibility factor, a constant satisfying $$c \ge \epsilon ^2$$ and $$\sin (\angle pp'v_j) \le 1/\sqrt{1+c}$$ , over all iterates $$p'$$ . In particular, the geometry of the input data may result in efficient complexities such as $$O(mn \root t \of {\epsilon ^{-2}} \ln \epsilon ^{-1})$$ , $$t$$ a natural number, or even $$O(mn \ln \epsilon ^{-1})$$ . Additionally, (i) we prove a strict distance duality and a related minimax theorem, resulting in more effective pivots; (ii) describe $$O(mn \ln \epsilon ^{-1})$$ -time algorithms that may compute a witness or a good approximate solution; (iii) prove generalized distance duality and describe a corresponding generalized Triangle Algorithm; (iv) prove a sensitivity theorem to analyze the complexity of solving LP feasibility via the Triangle Algorithm. The Triangle Algorithm is practical and competitive with the simplex method, sparse greedy approximation and first-order methods. Finally, we discuss future work on applications and generalizations. [ABSTRACT FROM AUTHOR]

Though a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can be of two types, making useful the distinction between Inherently Stationary and Inherently Non-Stationary Hermite subdivision schemes. This paper focuses on the class of inherently stationary, dual non-interpolatory Hermite subdivision schemes that can be obtained from known Hermite interpolatory ones, by applying a generalization of the de Rham corner cutting strategy. Exploiting specific tools for the analysis of inherently stationary Hermite subdivision schemes we show that, giving up the interpolation condition, the smoothness of the associated basic limit function can be increased by one, while its support width is only enlarged by one. To accomplish the analysis of de Rham-type Hermite subdivision schemes two new theoretical results are derived and the new notion of $$HC^{\ell }$$ -convergence is introduced. It allows the construction of Hermite-type subdivision schemes of order $$d+1$$ with the first element of the vector valued limit function having regularity $$\ell \ge d$$ . [ABSTRACT FROM AUTHOR]

We prove that for a topological space $$X$$ with the property that $$ H_{*}(U)=0$$ for $$*\ge d$$ and every open subset $$U$$ of $$X$$ , a finite family of open sets in $$X$$ has nonempty intersection if for any subfamily of size $$j,\,1\le j\le d+1,$$ the $$(d-j)$$ -dimensional homology group of its intersection is zero. We use this theorem to prove new results concerning transversal affine planes to families of convex sets. [ABSTRACT FROM AUTHOR]

We study the behavior of solutions for the parabolic equation of nonstationary diffusion with double nonlinearity and a degenerate absorption term: where $$ {a}_0(x)\ge {d}_0\; \exp \left(-\frac{\omega \left(\left| x\right|\right)}{{\left| x\right|}^{q+1}}\right) $$, d = const > 0, 0 ≤ λ < q, ω(⋅) ϵ C([0, + ∞)), ω(0) = 0, ω( τ) > 0 for τ > 0, and $$ {\displaystyle {\int}_{0+}\frac{\omega \left(\tau \right)}{\tau} d\tau <\infty } $$. By the local energy method, we show that a Dini-type condition imposed on the function ω(·) guarantees the decay of an arbitrary solution for a finite period of time. [ABSTRACT FROM AUTHOR]

A cutting-plane procedure for integer programming (IP) problems usually involves invoking a black-box procedure (such as the Gomory-Chvátal procedure) to compute a cutting-plane. In this paper, we describe an alternative paradigm of using the same cutting-plane black-box. This involves two steps. In the first step, we design an inequality $$cx \le d$$ where $$c$$ and $$d$$ are integral, independent of the cutting-plane black-box. In the second step, we verify that the designed inequality is a valid inequality by verifying that the set $$P \cap \{x\in \mathbb R ^n \mid cx \ge d + 1\} \cap \mathbb Z ^n$$ is empty using cutting-planes from the black-box. Here $$P$$ is the feasible region of the linear-programming relaxation of the IP. We refer to the closure of all cutting-planes that can be verified to be valid using a specific cutting-plane black-box as the verification closure of the considered cutting-plane black-box. This paper undertakes a systematic study of properties of verification closures of various cutting-plane black-box procedures. [ABSTRACT FROM AUTHOR]

In this study, the production methods and the applications of As are reviewed with special attention to the feasibility of the cyclotron production of As. TALYS-1.4 and ALICE/ASH codes were employed to illustrate the formation of the As via Ge( p, xn)As, Ge( p, xn)As, Ge( d, 2 n)As, and Ga( α, n)As reactions. Hybrid model and geometry dependent hybrid model were used in ALICE/ASH code to calculate the pre-equilibrium neutron-production cross sections. The excitation functions of the reactions were taken from the TENDL-2011 database and compared with the reported experimental measurement. The equilibrium and pre-equilibrium effects on the reactions were also discussed. An optimum energy range and the level of impurities for each reaction were determined. The As production yield was evaluated with concentration on the excitation function calculations and the stopping powers of the projectiles in the targets. [ABSTRACT FROM AUTHOR]

Adverse effects on the pulmonary circulation in obstructive sleep disordered breathing (SDB) may place children with heart lesions affecting the right ventricle at increased risk for morbidity and mortality. We examined the distribution and effects of SDB in pediatric patients with tetralogy of Fallot (TOF). Families of 37 pediatric patients with TOF completed a survey of cardiac symptoms and school performance as well as a Pediatric Sleep Questionnaire (PSQ), a validated questionnaire for the screening of SDB in children 2–18 years of age. Medical records were reviewed for growth parameters, medical history, and most recent electrocardiogram (ECG) findings. Data from patients with SDB (PSQ score ≥8, n = 14) were compared to data from patients without SDB (PSQ score <8; n = 23). The prevalence of SDB in this population (38%) was significantly higher than the published prevalence of 5% in a healthy general pediatric population ( p < 0.001). No significant difference was found in age, gender, or age and sex standardized body mass index between patients with or without SDB. No difference was seen in medication use or timing of surgical repair, whether primary or palliative. Patients with SDB had a significantly higher cardiac symptom score ( p = 0.01) and increasing PSQ scores correlated with worsening cardiac symptom scores ( p = 0.006). Increasing PSQ scores also correlated with worsening school performance ( p = 0.001). No differences were seen in ECG data. The screened prevalence of SDB in the pediatric population with TOF is higher than in the general population; patients with TOF and SDB are more likely to have worse cardiac symptoms and poor school performance. [ABSTRACT FROM AUTHOR]

A pilot search for the excitation of [sup 73]Ge to the first excited state at 13.26 keV by spin-dependent interactions of Weakly Interacting Massive Particles (WIMPs) was performed. The first experimental results have been analyzed with a new method. The background for these reactions is ≤0.0012 events/(keV kg([sup 73]Ge) d). Although there is no theory for E2 excitations by WIMPs, this very large suppression of the background may promise an enlarged version of this experiment to be competitive. It is appropriate to propose an experiment with several kg of enriched [sup 73]Ge detectors based on these results. [ABSTRACT FROM AUTHOR]

Background:MicroRNA-7 (miR-7) has been reported to be a tumour suppressor gene. However, whether it has a role in the growth of non-small-cell lung cancer (NSCLC) and what is its target involved in the tumour growth is still under investigation.Methods:NSCLC tissue sample, NSCLC cell lines and tissue microarray were investigated in this study. Total RNA, miRNA and protein were used for RT-PCR and western blot analysis. Immunohistochemistry was performed in tissues microarray. Cell culture and intervention experiments were performed in vitro and in vivo. Bioinformatics prediction, western blot and luciferase assay were identified the target of miR-7.Results:In this study, we found that the expression of miR-7 was significantly downregulated not only in NSCLC cell lines, but also in human NSCLC tissues compared with the matched adjacent tissues. Restoration of its expression through miR-7 mimics in A549 and H1299 NSCLC cells inhibited cell proliferation, colony formation, and cell-cycle progression in vitro. More importantly, the tumorigenicity in nude mice was reduced after administration of miR-7 in vivo. In advance, through bioinformatic analysis, luciferase assay and western blot, we identified a novel target of miR-7, PA28gamma (a proteasome activator) to be enrolled in the regulation with tumour. PA28gamma mRNA and protein levels are markedly upregulated in NSCLC cell lines and tumour samples, exhibiting a strong inverse relation with that of miR-7. In addition, knockdown of PA28gamma induced similar effects as overexpression of miR-7 in NSCLC cells. Furthermore, miR-7 overexpression or silencing of PA28gamma reduced the cyclinD1 expression at mRNA and protein level in NSCLC cell lines.Conclusion:All these findings strongly imply that the overexpression of PA28gamma resulted from miR-7 downexpression in NSCLC has an important role in promoting cancer cell progress and consequently results in NSCLC growth. Thus, strategies targeting PA28gamma and/or miR-7 may become promising molecular therapies in NSCLC treatment. [ABSTRACT FROM AUTHOR]

During accident, the interlayer of windshield plays an important role in the crash safety of automotive and protection of pedestrian or passenger. The understanding of its energy absorption capability is of fundamental importance. Conventional interlayer material of automotive windshield is made by Polyvinyl butyral (PVB). Recently, a new candidate of high-performance nanoporous energy absorption system (NEAS) has been suggested as a candidate for crashworthiness. For the model problem of pedestrian head impact with windshield, we compare the energy absorption capabilities of PVB and NEAS interlayers, in terms of the contact force, acceleration, velocity, head injury criteria, and energy absorption ratio, among which results obtained from PVB interlayers are validated by literature references. The impact speed is obtained from virtual test field in PC-CRASH, and the impact simulations are carried out using explicit finite element simulations. Both the accident speed and interlayer thickness are varied to explore their effects. The explicit relationships established among the energy absorption capabilities, impact speed, and interlayer material/thickness, are useful for safety evaluation as well as automotive design. It is shown that the NEAS interlayer may absorb more energy than PVB interlayer and it may be a competitive candidate for windshield interlayer. [ABSTRACT FROM AUTHOR]