On a family of copulas constructed from the diagonal section

We characterize the class of copulas that can be constructed from the diagonal section by means of the functional equation C(x,y)+|x−y|=C(x∨y,x∨y), for all (x,y) in the unit square such that C(x,y)>0. Some statistical properties of this class are given.     

Crown graphs and subdivision of ladders are odd graceful

A graph G of size q is odd graceful, if there is an injection φ from V(G) to {0, 1, 2, …, 2q?1} such that, when each edge xy is assigned the label or weight |f(x)?f(y)|, the resulting edge labels are {1, 3, 5, …, 2q?1}. This definition was introduced in 1991 by Gnanajothi [3], who proved that the graphs obtained by joining a single pendant edge to each vertex of C _n are odd graceful, if n is even. In this paper, we generalize Gnanajothi's result on cycles by showing that the graphs obtained by joining m pendant edges to each vertex of C _n are odd graceful if n is even. We also prove that the subdivision of ladders S(L _n ) (the graphs obtained by subdividing every edge of L _n exactly once) is odd graceful.     

Panconnectivity and edge-pancyclicity of 3-ary <Emphasis Type="Italic">N</Emphasis>-cubes

We study two topological properties of the 3-ary n-cube Q _n ³. Given two arbitrary distinct nodes x and y in Q _n ³, we prove that there exists an x–y path of every length ranging from d(x,y) to 3 ⁿ −1, where d(x,y) is the length of a shortest path between x and y. Based on this result, we prove that Q _n ³ is edge-pancyclic by showing that every edge in Q _n ³ lies on a cycle of every length ranging from 3 to 3 ⁿ .

NiCrAlY薄膜应变计的研制

采用射频磁控溅射法在Ni基高温合金拉伸件上制备NiCrAlY薄膜应变计。研究了热稳定处理对NiCrAlY薄膜结构、表面形貌的影响,并且测试了NiCrAlY薄膜应变计的电学与应变性能。结果表明：热稳定处理后 NiCrAlY 薄膜应变计由于在表面形成了一层 Al2 O3膜,具有抗高温氧化的特性,在室温～800℃范围内,应变计电阻同温度呈线性变化,电阻温度系数（ TCR）约为290×10－6/℃,室温下的应变计系数（ GF）为2.1。     

A general method to derive implicit equations of curves and surfaces using interlineation and interflation of functions

A general method is proposed to derive equations of irregular curves O _D (x, y) = 0 and of irregular surfaces O _G (x, y, z) =0 in implicit form, where the functions O _D (x, y) and O _G (x, y, z) belong to a prescribed differentiability class. The method essentially involves interlineation and interflation of functions. An example is considered.     

Lanczos <Emphasis Type="Italic">τ</Emphasis>-method regularization algorithm and its algebraic-programming implementation

An algebraic algorithm is developed for computing an algebraic polynomial y _n of order n ∈ N in computer algebra systems. This polynomial is the optimal approximation of the solution y = y(x), x ∈ [a,b], to a system of linear differential equations with polynomial coefficients and initial conditions at a regular singular zero point of this equation in a space C_{[ a,b ]}^k C_{\left[ {a,b} \right]}^k .     

The multiple loop antenna for enhanced readability performances of near‐field UHF RFID applications

This research is concerned with a multiple loop antenna applicable to near field ultra‐high frequency (UHF) radio frequency identification (RFID). The proposed multi‐loop antenna is configured to induce the robust and even magnetic field distributions in the H_x, H_y, and H_z orientations so as to achieve the enhanced readability performances in all directions (i.e., x, y, and z). Simulations were carried out using CST Microwave Studio to determine the impedance bandwidth (|S₁₁|H_x‐, H_y‐, and H_z‐oriented magnetic field distributions. A prototype antenna of 14 cm × 16 cm × 0.6 mm (W × L × H) in overall dimension was subsequently fabricated on an FR4 substrate connected to a coaxial cable. In this research, the H_x‐, H_y‐, and H_z‐oriented magnetic field distributions of the prototype antenna were measured in the x‐axis, y‐axis, and x–y plane and are in good agreement with the simulation results. The measured readability performances in the x‐, y‐, and z‐directions in which seven near field UHF RFID tags were deployed unobstructed (i.e., in open air) are respectively 25.27%, 31.73%, and 85.43%. Furthermore, the performances on the antenna readability with the tags attached to the microcentrifuge tubes are 30.55%, 25.90%, and 69.09% for the x‐, y‐, and z‐directions. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:402–417, 2016.     

Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An Efficient Algorithm

In many problems in science and engineering ranging from astrophysics to geosciences to financial analysis, we know that a physical quantity y depends on the physical quantity x, i.e., y = f(x) for some function f(x), and we want to check whether this dependence is monotonic. Specifically, finitely many measurements of x_i and y = f(x) have been made, and we want to check whether the results of these measurements are consistent with the monotonicity of f(x). An efficient parallelizable algorithm is known for solving this problem when the values x_i are known precisely, while the values y_i are known with interval uncertainty. In this paper, we extend this algorithm to a more general (and more realistic) situation when both x_i and y_i are known with interval uncertainty.     

On the structure of multivariate concentration — some relationships among the concentration surface and two variate mean difference and regressions

First, concentration surface L(x, y) and Gini's coefficient G_xy with respect to two variates x and y are defined and discussed. Mean difference Δ_xy and mean deviation δ_xy of x and y are also defined in connection with L(x,y) and G_xy. Some other statistical measures working like correlation coefficient and regression coefficient are newly introduced based on the geometrical properties of the concentration surface and are discussed in comparison with moment measures corresponding to them.Non-linear regression is also discussed based on certain representative income distributions.The close relations between Gini's coefficient G_xy and the regression residuals are pointed out in the case of both linear and non-linear regressions.Finally, elasticity analysis is tried on the family budget data of Japan in 1981.     

A technique for monitoring SO2 in combustion exhausts: Use of a non-Nernstian sensing element in combination with an upstream catalytic filter

Detection of sulfur dioxide (SO₂) at high temperature (600–750 °C) in the presence of some interferents found in combustion exhausts (NO₂, NO, CO₂, CO, and hydrocarbon (C₃H₆)) is described. The detection scheme involves use of a catalytic filter in front of a non-Nernstian (mixed-potential) sensing element. The catalytic filter was a Ni:Cr powder bed operating at 850 °C, and the sensing elements were pairs of platinum (Pt) and oxide (Ba-promoted copper chromite ((Ba,Cu)_xCr_yO_z) or Sr-modified lanthanum ferrite (LSF)) electrodes on yttria-stabilized zirconia. The Ni:Cr powder bed was capable of reducing the sensing element response to NO₂, NO, CO, and C₃H₆, but the presence of NO₂ or NO (“NO_x”, at 100 ppm by volume) still interfered with the SO₂ response of the Pt–(Ba,Cu)_xCr_yO_z sensing element at 600 °C, causing approximately a 7 mV (20%) reduction in the response to 120 ppm SO₂ and a response equivalent to about 20 ppm SO₂ in the absence of SO₂. The Pt–LSF sensing element, operated at 750 °C, did not suffer from this NO_x interference but at the cost of a reduced SO₂ response magnitude (120 ppm SO₂ yielded 10 mV, in contrast to 30 mV for the Pt-(Ba,Cu)_xCr_yO_z sensing element). The powder bed and Pt–LSF sensing element were operated continuously over approximately 350 h, and the response to SO₂ drifted downward by about 7%, with most of this change occurring during the initial 100 h of operation.     

A new universal approximation result for fuzzy systems,which reflects CNF DNF duality

There are two main fuzzy system methodologies for translating expert rules into a logical formula: In Mamdani's methodology, we get a DNF formula (disjunction of conjunctions), and in a methodology which uses logical implications, we get, in effect, a CNF formula (conjunction of disjunctions). For both methodologies, universal approximation results have been proven which produce, for each approximated function f(x), two different approximating relations R_DNF(x, y) and R_CNF(x, y). Since, in fuzzy logic, there is a known relation F_CNF(x) ≤ F_DNF(x) between CNF and DNF forms of a propositional formula F, it is reasonable to expect that we would be able to prove the existence of approximations for which a similar relation R_CNF(x, y) ≤ R_DNF(x, y) holds. Such existence is proved in our paper. © 2002 Wiley Periodicals, Inc.     

Surface modification of a-Si<Subscript>0.60</Subscript>C<Subscript>0.40</Subscript>:H films by Al-assisted photochemical etching: humidity sensing application

The paper investigates the formation of thin porous amorphous silicon carbide (PASiC) by Al-assisted photochemical etching using HF/AgNO₃ solution under UV illumination at λ = 254 nm. Different etching times varying from 2 to 10 min have been used on thin a-Si_0.60C_0.40:H films, which are elaborated by co-sputtering DC magnetron using a single crystal Si target and who deposited onto 86 of hot pressed polycrystalline 6H-SiC stripes of 12.5 mm³. Because of the high electrical resistivity of the thin a-Si_0.60C_0.40:H film higher than 2 MΩ cm, and in order to facilitate the chemical etching, a thin metallic film of high purity aluminum (Al) has been deposited under vacuum, follow-up of a thin palladium deposited under a grid to reduce attacked surface and reinforced solution etching. The etched surface was characterized by scanning electron microscopy, infrared spectroscopy, spectrophotometer UV, and photoluminescence. Results show that the morphology of etched a-Si_0.60C_0.40:H surface evaluates with etching time and presents a spongy and macroporous layers. Where, the diameter of pore size increases with the increasing etching time. A humidity sensors were fabricated through evaporating coplanar interdigital gold electrodes on PASiC and the humidity sensing properties were tested, it show, that the measured resistance Au-PASiC structure, depends highly on the applied bias voltage. Finally, the sensing performances are attributed to the unique surface structure, morphology of the pore and its size, that provide an effective pathway for vapor transportation and enlarged the sensing area of Au-PASiC.     

Nanowire structured SnOx–SWNT composites: High performance sensor for NOx detection

A nanowire structured nanocomposite of tin oxide (SnO_x) and a single-walled carbon nanotube (SWNT) are fabricated using rheotaxial growth and thermal oxidation method for gas sensor application. The morphology, gas sensing properties, as well as the chemical and electrical properties are investigated. The oxidation temperature for Sn mainly determines the stoichiometry of the SnO_x nano-beads, and consequently the electrical and gas sensing properties of the nanocomposite sensors. The gas sensing to nitrogen oxide, hydrogen, oxygen, xylene, acetone, carbon monoxide, and ammonia are also examined to determine the gas selectivity of the sensor. The high sensitivity and selectivity towards NO_x of the nanocomposite sensor is realized via the porous structure of the SWNT template. The gas sensing mechanism of the nanocomposite structure is also discussed.     

Interpolazione con splines verificanti una opportuna condizione

Summary A partition of the interval [x ₀,x _n+1] inton+1 subintervals [x _i ,x _i+1] (i=0,1,...,n) is considered. A spline functionf(x)∈C ^m , which coincides with a polynomialp _i (x)[p _i (x _i )=y _i ,p _i (x _i+1)=y _i+1] of degreem+1 in [x _i ,x _i+1 ], is introduced. Such a spline depends onm arbitrary constants. These constants are determined minimizing the integral .      

A class of hybrid collocation methods for third-order ordinary differential equations

A class of numerical methods is proposed for solving general third-order ordinary differential equations directly by collocation at the grid points x = x _n+j , i = 0(1)k and at an off grid point x = x _n+u , where k is the step number of the method and u is an arbitrary rational number in (x _n , x _n+k ). A predictor of order 2k ? 1 is also proposed to cater for y _n+k in the main method. Taylor series expansion is employed for the calculation of y _n+1, y _n+2, y _n+u and their higher derivatives. Evaluation of the resulting method at x = x _n+k for any value of u in the specified open interval yields a particular discrete scheme as a special case of the method. The efficiency of the method is tested on some general initial value problems of third-order ordinary differential equations.     

Bounded dilation maps of hypercubes into Cayley graphs on the symmetric group

LetG andH be graphs with |V(G)≤ |V(H)|. Iff:V(G) →V(H) is a one-to-one map, we letdilation(f) be the maximum of dist _H (f x),f(y)) over all edgesxy inG where dist _H denotes distance inH. The construction of maps fromG toH of small dilation is motivated by the problem of designing small slowdown simulations onH of algorithms that were originally designed for the networkG. LetS(n), thestar network of dimension n, be the graph whose vertices are the elements of the symmetric group of degreen, two verticesx andy being adjacent ifx o (1,i) =y for somei. That is,xy is an edge ifx andy are related by a transposition involving some fixed symbol (which we take to be 1). Also letP(n), thepancake network of dimension n, be the graph whose vertices are the elements of the symmetric group of degreen, two verticesx andy being adjacent if one can be obtained from the other by reversing some prefix. That is,xy is an edge ifx andy are related byx o (1,i(2,i-1) ⋯ ([i/2], [i/2]) =y. The star network (introduced in [AHK]) has nice symmetry properties, and its degree and diameter are sublogarithmic as functions of the number of vertices, making it compare favorably with the hypercube network. These advantages ofS(n) motivate the study of how well it can simulate other parallel computation networks, in particular, the hypercube. The concern of this paper is to construct low dilation maps of hypercube networks into star or pancake networks. Typically in such problems, there is a tradeoff between keeping the dilationsmall and simulating alarge hypercube. Our main result shows that at the cost ofO (1) dilation asn→ ∞, one can embed a hypercube of near optimum dimension into the star or pancake networksS(n) orP(n). More precisely, lettingQ (d) be the hypercube of dimensiond, our main theorem is stated below. For simplicity, we state it only in the special case when the star network dimension is a power of 2. A more general result (applying to star networks of arbitrary dimension) is obtained by a simple interpolation. This author's research was done during the Spring Semester 1991, as a visiting professor in the Department of Mathematics and Statistics at Miami University.     

On estimation of the probability of absence of collisions of some random mappings

Let X and Y be finite sets and φ: (X,Y) →Y be a mapping. Consider a random mapping i → φ(x_i,y_i), where x_i are arbitrarily chosen from the set X, whereas (y_i) is a random sample from Y without replacement. A two-sided bound is derived for the probability of absence of collisions of this mapping. A case of mapping, defined as φ(x, y)=x+ y modulo n, is considered in particular. The results may be used in the selection of identification codes. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 132–137, January–February, 2000.     

Embedding of Cycles in Twisted Cubes with Edge-Pancyclic

In this paper, we study the embedding of cycles in twisted cubes. It has been proven in the literature that, for any integer l, 4≤l≤2 ⁿ , a cycle of length l can be embedded with dilation 1 in an n-dimensional twisted cube, n≥3. We obtain a stronger result of embedding of cycles with edge-pancyclic. We prove that, for any integer l, 4≤l≤2 ⁿ , and a given edge (x,y) in an n-dimensional twisted cube, n≥3, a cycle C of length l can be embedded with dilation 1 in the n-dimensional twisted cube such that (x,y) is in C in the twisted cube. Based on the proof of the edge-pancyclicity of twisted cubes, we further provide an O(llog l+n ²+nl) algorithm to find a cycle C of length l that contains (u,v) in TQ _n for any (u,v)∈E(TQ _n ) and any integer l with 4≤l≤2 ⁿ .     

Calculation of precipitation behaviour in an alloy steel using a thermochemical data bank and the program ‘solgasmix’

The precipitates forming in an alloy steel at different carbon and nitrogen concentrations and at different temperatures have been calculated. The calculations have been carried out using the computer program SOLGASMIX in association with thermochemical values retrieved automatically from a data bank. The results provide information on the stabilities and amounts of the precipitated phases and also on the stoichiometry of the carbonitride phase Nb(C_xN_y).