Search

A new trapezoid-shaped Frisch-grid ionization chamber (TFG-IC) has been built as a part of a $$\varDelta {E}-E$$ Δ E - E telescope system for the detection and identification of charged particles at energies down to a few MeV. To study the effect of the drift electric field uniformity, two types of sealed windows, namely a pair of SSA (split-strip aluminized mylar film) and a pair of DSA (double-sided aluminized mylar film) sealed windows have been investigated. The detector’s performances were studied using a standard $$^{241}$$ 241 Am source at different gas pressures, and the total energy-deposit resolution achieved is about 1.1%(FWHM). The $$\varDelta {E}-E$$ Δ E - E telescope, which was composed of TFG-IC and a DSSSD (double-sided silicon strip detector), has been tested using a three-component $$\alpha $$ α source and the $$^{241}$$ 241 Am source under laboratory conditions. The results show that the energy resolution with the SSA sealed windows which provide uniform drift electric field has a smaller fluctuation than that with the DSA ones; the fluctuations are about 1% and 4% for the former and the latter, respectively. Simulations using the COMSOL software also confirmed the electric-field distortion at the edge of the detector with the DSA windows. A correlation curve between energy resolution and energy deposit of charged particles at various gas pressures and for two gas species is derived for TFG-IC with the SSA sealed windows using the measurement with the $$^{241}$$ 241 Am source. Incorporating the above results, we performed Monte Carlo simulations to evaluate the particle-identification capability of the telescope. The results show that the telescope can be extended to the identification of low-energy particles.

International audience

In a graph $G=(V,E)$, each vertex $v\in V$ is labelled with $0$, $1$ or $2$ such that each vertex labelled with $0$ is adjacent to at least one vertex labelled $2$ or two vertices labelled $1$. Such kind of labelling is called an Italian dominating function (IDF) of $G$. The weight of an IDF $f$ is $w(f)=\sum_{v\in V}f(v)$. The Italian domination number of $G$ is $\gamma_{I}(G)=\min_{f} w(f)$. Gao et al. (2019) have determined the value of $\gamma_I(P(n,3))$. In this article, we focus on the study of the Italian domination number of generalized Petersen graphs $P(n, k)$, $k\neq3$. We determine the values of $\gamma_I(P(n, 1))$, $\gamma_I(P(n, 2))$ and $\gamma_I(P(n, k))$ for $k\ge4$, $k\equiv2,3(\bmod5)$ and $n\equiv0(\bmod5)$. For other $P(n,k)$, we present a bound of $\gamma_I(P(n, k))$. With the obtained results, we partially solve the open problem presented by Bre\v{s}ar et al. (2007) by giving $P(n,1)$ is an example for which $\gamma_I=\gamma_{r2}$ and characterizing $P(n,2)$ for which $\gamma_I(P(n,2))=\gamma_{r2}(P(n,2))$. Moreover, our results imply $P(n,1)$ $(n\equiv0(\bmod\ 4))$ is Italian, $P(n,1)$ $(n\not\equiv0(\bmod\ 4))$ and $P(n,2)$ are not Italian.

The crossing number of a graph G is the minimum number of pairwise intersections of edges in a drawing of G . Motivated by the recent work (Faria et al., 2008) which solves the upper bound conjecture on the crossing number of n -dimensional hypercube proposed by Erdős and Guy, we consider the crossing number of locally twisted cubes L T Q n , which is one of important variation of the hypercube Q n . In this paper, we obtain the upper bound of the crossing number of L T Q n as follows. c r ( L T Q n ) ≤ 87 512 4 n − 4 n 2 − 15 + ( − 1 ) n − 1 32 2 n .

The previous study has shown that the mechanical properties of extruded Mg–Zn–Al–Sn alloys decrease with the increasing of extrusion temperature because of the coarsened microstructure. In order to improve the microstructure of Mg–Zn–Al–Sn alloy extruded at a high temperature, a small amount of Mn (0.6 wt%) was added to Mg–4Zn–2Al–2Sn (ZAT422, wt%) alloy in the present study, and ZAT422 and Mg–4Zn–2Al–2Sn–0.6Mn (ZATM4220, wt%) alloys were extruded into bars with 16 mm in diameter at an extrusion temperature of 648 K. Then the microstructures and mechanical properties of ZAT422 and ZATM4220 alloys were examined. It was found that the extruded ZATM4220 alloy exhibited finer deformation microstructure and better mechanical properties than ZAT422 alloy.

It is known widely that an interconnection network can be denoted by a graph G = ( V , E ) , where V denotes the vertex set and E denotes the edge set. Investigating structures of G is necessary to design a suitable topological structure of interconnection network. One of the critical issues in evaluating an interconnection network is graph embedding, which concerns whether a host graph contains a guest graph as its subgraph. Linear arrays (i.e., paths) and rings (i.e., cycles) are two ordinary guest graphs (or basic networks) for parallel and distributed computation. In the process of large-scale interconnection network operation, it is inevitable that various errors may occur at nodes and edges. It is significant to find an embedding of a guest graph into a host graph where all faulty nodes and edges have been removed. This is named as fault-tolerant embedding. The twisted hypercube-like networks ( T H L N s ) contain several important hypercube variants. This paper is concerned with the fault-tolerant path-embedding of n-dimensional (n-D) T H L N s . Let G n be an n-D T H L N and F be a subset of V ( G n ) &cup, E ( G n ) with | F | &le, n - 2 . We show that for two different arbitrary correct vertices u and v, there is a faultless path P u v of every length l with 2 n - 1 - 1 &le, l &le, 2 n - f v - 1 - &alpha, where &alpha, = 0 if vertices u and v form a normal vertex-pair and &alpha, = 1 if vertices u and v form a weak vertex-pair in G n - F ( n &ge, 5 ).

A Roman domination function on a graph G=(V(G),E(G)) is a function f:V(G)->{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. The weight of a Roman dominating function is the value f(V(G))[email protected]?"u"@?"V"("G")f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. Cockayne et al. [E. J. Cockayne et al. Roman domination in graphs, Discrete Mathematics 278 (2004) 11-22] showed that @c(G)@[email protected]"R(G)@[email protected](G) and defined a graph G to be Roman if @c"R(G)[email protected](G). In this article, the authors gave several classes of Roman graphs: P"3"k,P"3"k"+"2,C"3"k,C"3"k"+"2 for k>=1, K"m","n for min{m,n} 2, and any graph G with @c(G)=1; In this paper, we research on regular Roman graphs and prove that: (1) the circulant graphsC(n;{1,3})(n>=7,[email protected]?=4(mod5)) and C(n;{1,2,...,k})([email protected][email protected][email protected]?), [email protected]?=1 (mod (2k+1)), (n 2k) are Roman graphs, (2) the generalized Petersen graphs P(n,2k+1)(n 4k+2,n=0 (mod 4) and [email protected][email protected][email protected][email protected]?), P(n,1) ([email protected]?=2 (mod 4)), P(n,3) (n>=7,[email protected]?=3 (mod 4)) and P(11,3) are Roman graphs, and (3) the Cartesian product graphs C"5"[email protected]?C"5"n(m>=1,n>=1) are Roman graphs.

The equitable total chromatic number of a graph G is the smallest integer k for which G has a k-total coloring such that the number of vertices and edges colored with each color differs by at most one. In this paper, we show that the Cartesian product graphs of C"m and C"n have equitable total 5-coloring for all m>=3 and n>=3.

The planar Ramsey number PR ( H 1 , H 2 ) is the smallest integer n such that any planar graph on n vertices contains a copy of H 1 or its complement contains a copy of H 2 . It is known that the Ramsey number R ( C 4 , K 7 ) = 22 . The planar Ramsey numbers PR ( C 4 , K l ) for l ≤ 6 are known. In this paper we show that PR ( C 4 , K 7 ) = 20 .

Ringeisen and Beineke have proved that cr(C"[email protected]?C"n)=n and cr(K"[email protected]?C"n)=3n. Bokal has proved that cr(K"1","[email protected]?P"n)=(n-1)@[email protected][email protected][email protected]?. In this paper we study the crossing numbers of K"[email protected]?C"n and K"m","[email protected]?P"n, and show (i) cr(K"[email protected]?C"n)>=n.cr(K"m"+"2) for n>=3 and m>=5; (ii) cr(K"[email protected]?C"n)==8 with even n>=4, and equality holds for m=5,6,7 and for m=8,9,10 with even n>=4 and (iii) cr(K"m","[email protected]?P"n)= =2, and equality holds for min(m,l)=2.

Crossing numbers of graphs are in general very difficult to compute. There are several known exact results on the crossing number of the Cartesian products of paths, cycles or stars with small graphs. In this paper we study cr(Km □ Pn), the crossing number of the Cartesian product Km □ Pn. We prove that $$cr(K_{m} \square P_n)\leq \frac{1}{4}\lfloor\frac{m+1}{2}\rfloor\lfloor\frac{m-1}{2} \rfloor\lfloor\frac{m-2}{2}\rfloor(n\lfloor\frac{m+4}{2} \rfloor+ \lfloor\frac{m-4}{2}\rfloor)$$ for m ≥ 3,n ≥ 1 and cr(Km □ Pn)≥ (n − 1)cr(Km+2 − e) + 2cr(Km+1). For m≤ 5, according to Klesc, Jendrol and Scerbova, the equality holds. In this paper, we also prove that the equality holds for m = 6, i.e., cr(K6 □ Pn) = 15n + 3.

The planar Ramsey number PR(H"1,H"2) is the smallest integer n such that any planar graph on n vertices contains a copy of H"1 or its complement contains a copy of H"2. It is known that the Ramsey number R(K"4-e,K"5)=16. The planar Ramsey numbers PR(K"4-e,K"3)=7 and PR(K"4-e,K"4)=10 are known. In this paper we show that PR(K"4-e,K"5)=14.

Effects of different Al additions (3wt.%, 5wt.%, 7wt.%, 9wt.% Al) on as-cast microstructure and properties of Mg-Al-1Si-0.5Sr alloy were studied. The average grain size decreases and then increases with the increasing of Al additions. There are polyhedral shape, fine fibers shape, a few Chinese script Mg2Si particles and beta-Mg17Al12 divorced eutectic phase appeared in the interdendritic area in Mg-3Al-1Si-0.5Sr alloys. With the increase of Al content, more and more beta-Mg17Al12 divorced eutectic phase appear in semi-continuous distribution. The lamellar-like shape beta-Mg17Al12 secondary-precipitated phase emerge with Al addition of 5wt.%, 7wt.% and 9wt.%. The optimum tensile properties of Mg-7Al-1Si-0.5Sr alloy can be obtained, where the ultimate strength, yield strength and elongation are 201.1MPa, 160.7MPa, 4.8% at ambient temperature and 164.5MPa, 128.0MPa, 7.4% at 150 degrees C respectively. The hardness increased with the increasing of Al content.

Harary and Kovacs [Smallest graphs with given girth pair, Caribbean J. Math. 1 (1982) 24-26] have introduced a generalization of the standard cage question-r-regular graphs with given odd and even girth pair. The pair (@w,@e) is the girth pair of graph G if the shortest odd and even cycles of G have lengths @w and @e, respectively, and denote the number of vertices in the (r,@w,@e)-cage by f(r,@w,@e). Campbell [On the face pair of cubic planar graph, Utilitas Math. 48 (1995) 145-153] looks only at planar graphs and considers odd and even faces rather than odd and even cycles. He has shown that f(3,@w,4)[email protected] and the bounds for the left cases. In this paper, we show the values of f(r,@w,@e) for the left cases where (r,@w,@e)@?{(3,3,@e),(4,3,@e),(5,3,@e), (3,5,@e)}.

The multicolor Ramsey number R r (H) is defined to be the smallest integer n=n(r) with the property that any r-coloring of the edges of the complete graph K n must result in a monochromatic subgraph of K n isomorphic to H. It is well known that 2 r m

Calculating the crossing number of a given graph is, in general, an elusive problem. As Garey and Johnson have proved, the problem of determining the crossing number of an arbitrary graph is NP-complete (Crossing number is NP-complete, SIAM J. Alg. Disc. Meth. 4 (1983) 312-316). The crossing numbers of very few families of graphs are known exactly. Richter and Salazar (The crossing number of P(N,3), Graphs and Combinatorics 18 (2) (2002) 381-394) have studied the crossing number of the generalized Petersen graph P(n,3) and proved that cr(P(3h,3))=h(h>=4); cr(P(3h+1,3))=h+3(h>=3); cr(P(3h+2,3))=h+2(h>=3). In this paper, we study the crossing number of the circulant graph C(n;{1,3}) and prove that cr(C(n;{1,3}))[email protected]?n/[email protected]?+nmod3(n>=8).

Let $Q_n$ be the $n$-dimensional hypercube, and let ${\rm cr}(Q_n)$ be the \textit{crossing number} of $Q_n$. Erd��s and Guy in 1973 conjectured the following equality: ${\rm cr}(Q_n)=\frac{5}{32}4^n-\lfloor\frac{n^2+1}{2}\rfloor 2^{n-2}$. In this paper, we construct a drawing of $Q_n$ with less crossings when $n>6$, which implies that for $n>6$ we have a strict inequality., 44 pages; To appear in Journal of Graph Theory

The {\it crossing number} of a graph $G$ is the least number of pairwise crossings of edges among all the drawings of $G$ in the plane. The pancake graph is an important topology for interconnecting processors in parallel computers. In this paper, we prove the exact value of the crossing number of pancake graph $P_4$ is six., Comment: 10 pages, 11 figures

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. In this paper, we give the exact values of crossing numbers for some variations of hypercube with order at most four, including crossed cube, locally twisted cube and M\"{o}bius cube., Comment: 38 pages

The index of a graph is the largest eigenvalue of an adjacency matrix whose entries are the real numbers 0 and 1. Among the tricyclic Hamiltonian graphs with a prescribed number of vertices, those graphs with minimal index are determined.

The sound field in the melt processed by 20 kHz ultrasonic to fabricate CNT-AZ91D is investigated by numerical simulation. Firstly, the distribution of sound pressure in the AZ91D melt is calculated by the finite element method after the model of the sound filed of the ultrasonic processing has been built. The simulation results show that a radial sound field forms under the ultrasonic probe, which means that the sound pressure decreases with increasing distance from the sound source. After the sound field is revealed, we study the ultrasonic cavitation in the AZ91D melt with a single-bubbly-change model and examine the bubble change rule under different sound pressures by solving the Rayleigh-Plesset equation. The relationship between sound pressure amplitude and the ultrasonic cavitation in the melt is also discovered. The higher the sound pressure amplitude, the smaller the threshold radius for the bubble collapse is, and thus the ultrasonic cavitation in AZ91 melt happens more easily. Secondly, the sound fields of the melt with different immersed depths of the ultrasonic probe are calculated. The results show the optimal immersed depth is about 30 mm for the same crucible size used in the present study. Furthermore, the corresponding optimal immersed depth can be calculated for different crucible sizes or different melts by the present numerical method, which is important for the practical ultrasonic processing. After analyzing the calculated results for sound field and the cavitation rule of in the AZ91D synthetically, we find that the volume of the effective cavitation zone rapidly increases with the smaller ultrasonic power and then rises almost linearly with the ultrasonic power larger than 500 W. Finally, to verify the simulation method of the sound field, the contrast study between the simulation and experiment of ultrasonic processing using glycerol-water solution is performed. The simulation result of the sound field in glycerol-water solution is similar to that in AZ91D melt. The highest sound pressure occurs near the end face of ultrasonic probe, while the experimental observation shows that the strongest cavitation also happens near the end face of ultrasonic probe, which indicates that the highest sound pressure occurs in the zone.

The graph K5 - e is obtained from the complete graph K5 by deleting one edge, while K1 + C4 is obtained from K5 by deleting two independent edges. With the help of a computer it is shown that r(K1 + C4, K5 - e) = 17. © 1995 John Wiley & Sons, Inc.

A cast Mg-5Sn-4Zn-2Al alloy was developed by adding 2%Al and 4%Zn (mass fraction) into a Mg-5Sn base alloy. The results showed that the combined addition of Al and Zn had more obvious effect on dendrite refinement than the single Al addition. The single Al addition remarkably increased the elongation from 6.6% to 22.4%. With further addition of Zn, Mg32(Al, Zn)49 phase was introduced into the solidified microstructure, and the yield strength and ultimate tensile strength were increased to 96 and 232 MPa while elongation was decreased to 14.8%. After aging treatment at 175 for 24 h, there appeared peak hardness of 83.5 HV by forming the rod-shaped MgZn2 along c-axis and cubic Mg2Sn precipitates into �-Mg matrix for Mg-5Sn-4Zn-2Al alloy. With the aging strengthening, the yield strength and ultimate tensile strength were further increased to 144 and 264 MPa, respectively. When the testing temperature was elevated to 150 , the yield strength of peak-aged Mg-5Sn-4Zn-2Al alloy still attained to 138 MPa, which indicated that both the MgZn2 and Mg2Sn precipitates possess good thermal stability for elevated temperature property.

Based on the model for calculating the critical cooling rate of bulk metallic glasses under non-isothermal condition, a new model for calculating the critical cooling rate of alloy systems based on viscosity calculation is put forward in this paper. The critical cooling rates of Zr-Ni-Al-Cu quaternary alloys were calculated and the glass forming range in Zr 66.67 (Ni x Al y Cu z ) 33.33 quaternary alloy system is predicted. The results are in good agreement with the experimental values. The calculation results show that there is high glass forming ability in Zr 66.67 (Ni x Al y Cu z ) 33.33 quaternary alloy system. The glass forming range is near eutectic point in which critical cooling rates are less than 100 K/s. There is not crystallization in the temperature range higher than 1000K, the fraction of crystals increases rapidly in the temperature range from 980 K to 870 K, and it is not changed in the temperature range below 870 K. In addition, the effects of Al,Cu,Ni mole fraction on the critical cooling rate are analyzed in this paper.

Based on the non-isothermal transformation theory and non-steady state nucleatio n theory, a new method for calculating the continuous cooling transformation cur ve and the critical cooling rate of bulk metallic glass alloys is put forward in this paper. The continuous cooling transformation curves of Zr- and Pd-based al loys are calculated and the results are in good agreement with the experimental values. It is suggested that the method can be used to evaluate glass forming ab ility of alloy systems more effectively. In addition, the calculation results sh ow that the main factors effecting the critical cooling rate are the viscosity o f melt, nucleation barrier and critical volume fraction of the crystal, the crit ical cooling rate is reduced with the increase of the viscosity, nucleation barr ier and critical volume fraction of crystal.

Most wireless ad hoc networks consist of mobile devices which operate on batteries. Power consumption in this type of network therefore is paramount important. To maximize the lifetime of an ad hoc network, it is essential to prolong each individual node (mobile) life through minimizing the total transmission energy consumption for each communication request. Therefore, an efficient routing protocol must satisfy that the energy consumption rate at each node is evenly distributed and at the same time the total transmission energy for each request is minimized. To devise a routing protocol meeting the above two conflict objectives simultaneously is very difficult due to the NP hardness of the problem. Instead, an approximation solution is desirable and appreciated. In this paper, we focus on developing power-aware routing algorithms which find routing paths that maximize the lifetime of individual nodes and minimize the total transmission energy consumption, thereby prolong the life of the entire network. In particular, for an ad hoc network consisting of the same type of battery mobile nodes, two approximation algorithms are proposed. The running times of the proposed algorithms are determined by the accuracies of the approximation solutions. Compared with a previously known result, our algorithms have less energy overhead and can be implemented in a distributed environment. For an ad hoc network equipped with different types of battery mobile nodes, a new power-aware routing protocol is proposed, and the algorithm can also be implemented in a distributed manner.

The cooling rate has significant effects on the microstructure of Mg-Gd-Y-Zr alloy. It is found that the increase of cooling rate can refine the solidified microstructure obviously. The grains are refined and the morphology of the primary phases is changed from the coarse to the thin. With the increase of cooling rate, the eutectic distributes more homogeneously and its volume fraction decreases. Higher cooling rate can increase the solid solubility, which contributes to the reduction of dendritic segregation of solutes of Gd and Y in Mg-Gd-Y-Zr alloy.