Cyclic codes over $${\mathbb {F}}_{2^m}[u]/\langle u^k\rangle $$ of oddly even length

Let \({\mathbb {F}}_{2^m}\) be a finite field of characteristic 2 and \(R={\mathbb {F}}_{2^m}[u]/\langle u^k\rangle ={\mathbb {F}}_{2^m} +u{\mathbb {F}}_{2^m}+\ldots +u^{k-1}{\mathbb {F}}_{2^m}\) (\(u^k=0\)) where \(k\in {\mathbb {Z}}^{+}\) satisfies \(k\ge 2\). For any odd positive integer n, it is known that cyclic codes over R of length 2n are identified with ideals of the ring \(R[x]/\langle x^{2n}-1\rangle \). In this paper, an explicit representation for each cyclic code over R of length 2n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes over R of length 2n is obtained. Moreover, the dual code of each cyclic code and self-dual cyclic codes over R of length 2n are investigated.     

An illumination problem with tradeoff between coverage of a dataset and aperture angle of a conic light beam

Let \(\{a_i:i\in I\}\) be a finite set in \({\mathbb{R}}^n\). The illumination problem addressed in this work concerns the optimal location and orientation of a conic light beam

$$ R\big (z,y,s\big )= \left\{ x \in {\mathbb{R}}^n : s\,\Vert x-z\Vert - \langle y, x-z\rangle \le 0\right\} .$$

The aperture angle \(\vartheta = 2\arccos s\) of the conic light beam is a decreasing function of the sharpness coefficient \( s\in [0,1]\). The problem at hand is to select an apex z in a prescribed compact region \(Z\subseteq {\mathbb{R}}^n\) and a unit vector \(y\in {\mathbb{R}}^n\) so that the conic light beam R(z, y, s) fulfils two conflicting requirements: it captures as many points \(a_i\) as possible and, at the same time, it has a sharpness coefficient s as large as possible.

     

Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

Fanger’s predicted mean vote (PMV) equation is the result of the combined quantitative effects of the air temperature, mean radiant temperature, air velocity, humidity activity level and clothing thermal resistance. PMV is a mathematical model of thermal comfort which was developed by Fanger. The uncertainty budget of the PMV equation was developed according to GUM in this study. An example is given for the uncertainty model of PMV in the exemplification section of the study. Sensitivity coefficients were derived from the PMV equation. Uncertainty budgets can be seen in the tables. A mathematical model of the sensitivity coefficients of \(T_{\mathrm{a}}\), \(h_{\mathrm{c}}\), \(T_{\mathrm{mrt}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) is given in this study. And the uncertainty budgets for \(h_{\mathrm{c}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) are given in this study.     

A comparative study on dielectric behaviours of Au/(Zn-doped PVA)/<Emphasis Type="Italic">n</Emphasis>-4H-SiC (MPS) structures with different interlayer thicknesses using impedance spectroscopy methods

Three different thicknesses (50, 150 and 500 nm) Zn-doped polyvinyl alcohol (PVA) was deposited on n-4H-SiC wafer as interlayer by electrospinning method and so, Au/(Zn-doped PVA)/n-4H-SiC metal–polymer–semiconductor structures were fabricated. The thickness effect of Zn-doped PVA on the dielectric constant (\(\varepsilon ^{\prime }\)), dielectric loss (\(\varepsilon ^{{\prime }{\prime }}\)), loss-tangent (tan \(\delta \)), real and imaginary parts of electric modulus (\(M^{\prime }\) and \(M^{{\prime }{\prime }})\) and ac electrical conductivity \((\sigma _{\mathrm{ac}})\) of them were analysed and compared using experimental capacitance (C) and conductance (\(G/\omega \)) data in the frequency range of 1–500 kHz at room temperature. According to these results, the values of \(\varepsilon ^{\prime }\) and \(\varepsilon ^{{\prime }{\prime }}\) decrease with increasing frequency almost exponentially, \(\sigma _{\mathrm{ac}}\) increases especially, at high frequencies. The \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) values were obtained from the \(\varepsilon ^{\prime }\) and \(\varepsilon ^{{\prime }{\prime }}\) data and the \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) vs. f plots were drawn for these structures. While the values of \(\varepsilon ^{\prime }\), \(\varepsilon ^{{\prime }{\prime }}\) and tan \(\delta \) increase with increasing interlayer thickness, the values of \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) decrease with increasing interlayer thickness. The double logarithmic \(\sigma _{\mathrm{ac}}\) vs. f plots for each structure have two distinct linear regimes with different slopes, which correspond to low and high frequencies, respectively, and it is prominent that there exist two different conduction mechanisms. Obtained results were found as a strong function of frequency and interlayer thickness.     

High-pressure studies of superconductivity in $$\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}$$

\(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\) crystallizes in tetragonal CeOBiS\(_{2}\) structure (S. G. P4/nmm). We have investigated the effect of pressure on magnetization measurements. Our studies suggest improved superconducting properties in polycrystalline samples of \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\). The \(T_{\mathrm{c}}\) in our sample is 5.3 K, at ambient pressure, which is marginal but definite enhancement over \(T_{\mathrm{c}}\) reported earlier (= 5.1 K). The upper critical field \(H_{\mathrm{c}2}\)(0) is greater than 3 T, which is higher than earlier report on this material. As determined from the M–H curve, both \(H_{\mathrm{c}2}\) and \(H_{\mathrm{c}1}\) decrease under external pressure P (0 \(\le P \le \) 1 GPa). We observe a decrease in critical current density and transition temperature on applying pressure in \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\).     

Partial permutation decoding for MacDonald codes

We show how to find s-PD-sets of the minimal size \(s+1\) for the \(\left[ \frac{q^n-q^u}{q-1},n,q^{n-1}-q^{u-1}\right] _q \) MacDonald q-ary codes \(C_{n,u}(q)\) where \(n \ge 3\) and \(1 \le u \le n-1\). The construction of [6] can be used and gives s-PD-sets for s up to the bound \(\lfloor \frac{q^{n-u}-1}{(n-u)(q-1)} \rfloor -1\), of effective use for u small; for \(u \ge \lfloor \frac{n}{2} \rfloor \) an alternative construction is given that applies up to a bound that depends on the maximum size of a set of vectors in \(V_u(\mathbb {F}_q)\) with each pair of vectors distance at least 3 apart.     

Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, \(K_{\mathrm{IE},}\) was evaluated numerically as \(K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)\), where \(\upmu \) is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, \(K_{\mathrm{IE,d}}\), was observed to vary as \(K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}\). Consistent with the FEM simulation, experiments conducted using \(12\,\upmu \hbox {m}\) thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of \(\ge \) \(1.85\times 10^{9}\,\hbox {A/m}^{2}\) for \(a/w = 0.5\). Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.     

Bootstrap in semi-functional partial linear regression under dependence

This paper deals with the semi-functional partial linear regression model \(Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon \) under \(\alpha \)-mixing conditions. \({\varvec{\beta }} \in \mathbb {R}^{p}\) and \(m(\cdot )\) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates \({{\varvec{X}}}\) and \({\varvec{\chi }}\) are valued in \(\mathbb {R}^{p}\) and some infinite-dimensional space, respectively, and the random error \(\varepsilon \) verifies \(\mathbb {E}(\varepsilon |{{\varvec{X}}},{\varvec{\chi }})=0\). Naïve and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of \({\varvec{\beta }}\) and \(m(\chi )\), and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice.     

Nonparametric density and survival function estimation in the multiplicative censoring model

Consider the multiplicative censoring model given by \(Y_i=X_iU_i\), \(i=1, \ldots ,n\) where \((X_i)\) are i.i.d. with unknown density f on \({\mathbb {R}}\), \((U_i)\) are i.i.d. with uniform distribution \({\mathcal {U}}([0,1])\) and \((U_i)\) and \((X_i)\) are independent sequences. Only the sample \((Y_i)\) is observed. We study nonparametric estimators of both the density f and the corresponding survival function \(\bar{F}\). First, kernel estimators are built. Pointwise risk bounds for the quadratic risk are given, and upper and lower bounds for the rates in this setting are provided. Then, in a global setting, a data-driven bandwidth selection procedure is proposed. The resulting estimator has been proved to be adaptive in the sense that its risk automatically realizes the bias-variance compromise. Second, when the \(X_i\)s are nonnegative, using kernels fitted for \({\mathbb {R}}^+\)-supported functions, we propose new estimators of the survival function which are also adaptive. By simulation experiments, we check the good performances of the estimators and compare the two strategies.     

Aggregate packing and -void saturation in mortar and concrete proportioning

Proportioning was studied by measuring aggregate packing (C) and filling of aggregate void space (1?C) with varying volumes of cement paste (\(V_{\rm p}\)) or matrix (\(V_{\rm matrix}\)), i.e., all material <0.125 mm. Eleven widely different normal density aggregates with C = 0.57 to 0.71, i.e., aggregate void content (1?C) = 0.29 to 0.43, were used at constant w/c = 0.38 and flowing consistency and varying dosage of water reducer and paste- and matrix volume. Analysing plots of four excess phase volumes (paste with/without air, matrix with/without air) versus aggregate void space showed constant aggregate void saturation ratios. Both paste- and matrix-aggregate void saturation ratio can be used with the best estimate (\(V_{\rm p}-V_{\rm air})/{(1-C)}=1.15\) per \(\hbox{m}^{3}\). Including air voids in paste- or matrix volume improved correlation so air void content must be included in the normalized paste aggregate void saturation ratio (\(k=V_{\rm p}\)/[(1?C) \(V_{\rm tot}\)]). Simple measurements of aggregate packing are thus very useful. Cost per unit material, per unit fresh (slump, flow diameter) or hardened (compressive strength) property were used to show the cost efficiency of the mixes. The ranking of cost/MPa strength and cost/mm consistency is similar to ranking of total concrete cost for the 11 aggregates with a certain scatter though.     

Thermal Conductivity of Pyroclastic Soil (<Emphasis Type="BoldItalic">Pozzolana</Emphasis>) from the Environs of Rome

The paper reveals the experimental procedure and thermo-physical characteristics of a coarse pyroclastic soil (Pozzolana), from the neighborhoods of Rome, Italy. The tested samples are comprised of 70.7 % sand, 25.9 % silt, and 3.4 % clay. Their mineral composition contained 38 % pyroxene, 33 % analcime, 20 % leucite, 6 % illite/muscovite, 3 % magnetite, and no quartz content was noted. The effective thermal conductivity of minerals was assessed to be about \(2.14\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\). A transient thermal probe method was applied to measure the thermal conductivity (\(\lambda \)) over a full range of the degree of saturation \((S_{\mathrm{r}})\), at two porosities (n) of 0.44 and 0.50, and at room temperature of about \(25\,^{\circ }\hbox {C}\). The \(\lambda \) data obtained were consistent between tests and showed an increasing trend with increasing \(S_{\mathrm{r}}\) and decreasing n. At full saturation (\(S_{\mathrm{r}}=1\)), a nearly quintuple \(\lambda \) increase was observed with respect to full dryness (\(S_{\mathrm{r}}=0\)). In general, the measured data closely followed the natural trend of \(\lambda \) versus \(S_{\mathrm{r}}\) exhibited by published data at room temperature for other unsaturated soils and sands. The measured \(\lambda \) data had an average root-mean-squared error (RMSE) of \(0.007\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\) and \(0.008\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\) for n of 0.50 and 0.44, respectively, as well as an average relative standard deviation of the mean at the 95 % confidence level \((\hbox {RSDM}_{0.95})\) of 2.21 % and 2.72  % for n of 0.50 and 0.44, respectively.     

Characterization and optical properties of $$\hbox {Pr}_{2}\hbox {O}_{3}$$-doped molybdenum lead-borate glasses

\(\hbox {Pr}^{3+}\) doped molybdenum lead-borate glasses with the chemical composition 75PbO?[25–(x \(+\) y)\(\hbox {B}_{2}\hbox {O}_{3}]\)–\(y\hbox {MoO}_{3}\)–\(x\hbox {Pr}_{2}\hbox {O}_{3}\) (where \(x = 0.5\) and 1.0 mol% and \(y = 0\) and 5 mol%) were prepared by conventional melt-quenching technique. Thermal, optical and structural analyses are carried out using DSC, UV and FTIR spectra. The physical parameters, like glass transition \((T_{\mathrm{g}})\), stability factor \((\Delta T)\), optical energy band gap \((E_{\mathrm{gopt}})\), of these glasses have been determined as a function of dopant concentration. The \({T}_{\mathrm{g}}\) and optical energy gaps of these glasses were found to be in the range of 290–350\({^{\circ }}\hbox {C}\) and 2.45–2.7 eV, respectively. Stability of the glass doped with \(\hbox {Pr}^{3+}\) is found to be moderate (\(\sim \)40). The results are discussed using the structural model of Mo–lead-borate glass.     

Bracelet monoids and numerical semigroups

Given positive integers \(n_1,\ldots ,n_p\), we say that a submonoid M of \(({\mathbb N},+)\) is a \((n_1,\ldots ,n_p)\)-bracelet if \(a+b+\left\{ n_1,\ldots ,n_p\right\} \subseteq M\) for every \(a,b\in M\backslash \left\{ 0\right\} \). In this note, we explicitly describe the smallest \(\left( n_1,\ldots ,n_p\right) \)-bracelet that contains a finite subset X of \({\mathbb N}\). We also present a recursive method that enables us to construct the whole set \(\mathcal B(n_1,\ldots ,n_p)=\left\{ M|M \quad \text {is a} \quad (n_1,\ldots ,n_p)\text {-bracelet}\right\} \). Finally, we study \((n_1,\ldots ,n_p)\)-bracelets that cannot be expressed as the intersection of \((n_1,\ldots , n_p)\)-bracelets properly containing it.     

Numerical Study of Single Bubble Growth on and Departure from a Horizontal Superheated Wall by Three-dimensional Lattice Boltzmann Method

A three-dimensional hybrid lattice Boltzmann method was used to simulate the progress of a single bubble’s growth and departure from a horizontal superheated wall. The evolutionary process of the bubble shapes and also the temperature fields during pool nucleate boiling were obtained and the influence of the gravitational acceleration on the bubble departure diameter (BDD), the bubble release frequency (BRF) and the heat flux on the superheated wall was analyzed. The simulation results obtained by the present three-dimensional numerical studies demonstrate that the BDD is proportional to \(g^{\mathrm {-0.301}}\), the BRF is proportional to \(g^{\mathrm {-0.58}}\), and the averaged wall heat flux is proportional to \(g^{\mathrm {0.201}}\), where g is the gravitational acceleration. These results are in good agreement with the common-used experimental correlations, indicating the rationality of the present numerical model and results.     

Microstructure and Magnetic Properties of Sn<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ni<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>2</Subscript> Thin Films Prepared by Flash Evaporation Technique

An effort was made to develop semiconductor oxide-based room temperature dilute magnetic semiconductor (DMS) thin films based on wide band gap and transparent host lattice with transition metal substitution. The Sn\(_{\mathrm {1}-x}\)Ni\(_{x}\textit {O}_{\mathrm {2}}\) (\(x\,= \mathrm {0.00, 0.03, 0.05, 0.07, 0.10, and \,0.15}\)) thin film samples were prepared on glass substrates by flash evaporation technique. All the samples were shown single phase crystalline rutile structure of host SnO\(_{\mathrm {2}}\) with dominant (110) orientation. The Ni substitution promotes reduction of average crystallite size in SnO\(_{\mathrm {2}}\) as evidenced from the reduction of crystallite size from 40 (SnO\(_{\mathrm {2}}\)) to 20 nm (Sn\(_{\mathrm {0.85}}\)Ni\(_{\mathrm {0.15}}\textit {O}_{\mathrm {2}}\)). In the energy dispersive spectra as well as X-ray photoelectron spectra of all the samples show, the chemical compositions are close to stoichiometric with noticeable oxygen deficiency. The crystalline films were formed by coalescence of oval-shaped polycrystalline particles of 100 nm size as evidenced from the electron micrographs. The energy band gap of DMS films decreases from 4 (SnO\(_{\mathrm {2}}\)) to 3.8 eV (x \(=\) 0.05) with increase of Ni content. The magnetic hysteresis loops of all the samples at room temperature show soft ferromagnetic nature except for SnO\(_{\mathrm {2}}\) film. The SnO\(_{\mathrm {2}}\) films show diamagnetic nature and it converts into ferromagnetic upon substitution of 3 % Sn\(^{\mathrm {4+}}\) by Ni\(^{\mathrm {2+}}\). The robust intrinsic ferromagnetism (saturation magnetization, 21 emu/cm\(^{\mathrm {3}}\)). Further increase of Ni content weakens ferromagnetic strength due to Ni-O antiferromagnetic interactions among the nearest neighbour Ni ions via O\(^{\mathrm {2-}}\) ions. The observed magnetic properties were best described by bound magnetic polarons model.     

New formulations of the ship-motion Green function

The ship-motion Green function representing the potential flow generated by a time-harmonically pulsating source with unit strength advancing beneath a free surface along a straight path at a constant speed is studied in the paper. Starting with the form of a double Fourier integral with respect to wavenumber k and polar angle \(\theta \) on the Fourier plane, one alternative formulation based on the single integral along dispersion curves for the wave component, and the integrals in polar angle after having evaluated integration in wavenumber, is first presented. Another new formulation based on performing the integral with respect to polar angle \(\theta \) prior to the wavenumber k is developed afterward. Analytical formulations of the \(\theta \)-integral defined as \(g_{\ell }\left( k\right) \) are obtained by applying the theorem of residue. The behaviours of poles located in the integration contour are analyzed, and a method to efficiently evaluate the integral of \(g_{\ell }\left( k\right) \) for different values of Brard number \(\tau \) is outlined. Furthermore, numerical calculation is implemented. On comparing with the results obtained by means of the existing formulation, an excellent agreement is achieved with a maximum of difference in the order of \(10^{-6}\) which shows that two formulations are intrinsically consistent. The new formulation based on the polar angle integration is shown to be suitable for the study of the spatial integration of the Green function.     

Thermal Properties of Jojoba Oil Between $$20\,{^{\circ }}\hbox {C}$$ and $$45\,{^{\circ }}\hbox {C}$$45∘C

Vegetable oils have been widely studied as biofuel candidates. Among these oils, jojoba (Simmondsia chinensis) oil has attracted interest because it is composed almost entirely of wax esters that are liquid at room temperature. Consequently, it is widely used in the cosmetic and pharmaceutical industries. To date, research on S. chinensis oil has focused on to its use as a fuel and its thermal stability, and information about its thermal properties is scarce. In the present study, the thermal effusivity and conductivity of jojoba oil between \(20\,{^{\circ }}\hbox {C}\) and \(45\,{^{\circ }}\hbox {C}\) were obtained using the inverse photopyroelectric and hot-ball techniques. The feasibility of an inverse photopyroelectric method and a hot-ball technique to monitor the thermal conductivity, and the thermal effusivity of the S. chinensis is demonstrated. The thermal effusivity decreased from 538 \(\hbox {W}\cdot \,\hbox {s}^{1/2}\cdot \,\hbox {m}^{-2}\cdot \,\hbox {K}^{-1}\) to 378 \(\hbox {W}\cdot \,\hbox {s}^{1/2}\cdot \,\hbox {m}^{-2}\cdot \,\hbox {K}^{-1}\) as the temperature increased, whereas the thermal conductivity remained the same over the temperature range investigated in this study. The obtained results provide insight into the thermal properties of S. chinensis oil between \(20\,{^{\circ }}\hbox {C}\) and \(45\,{^{\circ }}\hbox {C}\).