Speeding up Huff form of elliptic curves

This paper presents faster inversion-free point addition formulas for the curve \(y (1+ax^2) = cx (1+dy^2)\). The proposed formulas improve the point doubling operation count record (I, M, S, D, a are arithmetic operations over a field. I: inversion, M: multiplication, S: squaring, D: multiplication by a curve constant, a: addition/subtraction) from \(6\mathbf{{M}}+ 5\mathbf{{S}}\) to \(8\mathbf{{M}}\) and mixed addition operation count record from \(10\mathbf{{M}}\) to \(8\mathbf{{M}}\). Both sets of formulas are shown to be 4-way parallel, leading to an effective cost of \(2\mathbf{{M}}\) per either of the group operations.     

Ring opening of epoxides with NaHSO4: isolation of β-hydroxy sulfate esters and an effective synthesis for trans-diols

Sodium hydrogen sulfate (NaHSO₄) was observed to be highly effective as a reagent or catalyst in the ring-opening reactions of epoxides under mild conditions. Reaction of epoxides with NaHSO₄ gave isolable β-hydroxy sulfate esters and vicinal diols. Experimenting with different epoxides, the study investigated the scope of the ring-opening reaction.     

On the stability of linear conservative gyroscopic systems

A simple criterion concerning the stability of linear gyroscopic conservative systems is developed. First, a sufficient condition for stability is established. The proof is based on a transformation converting the original autonomous system into a nonautonomous system, and applying Liapunov's direct method to the latter. Then a theorem is given which provides a necessary and sufficient condition for a restricted class of systems. Illustrative examples are provided.     

一种构造高维Nilpotent正规型的方法

正规型方法是一种有效的简化一类非线方程的方法。今提出了一种简便的代数方法去构造高维非线性系统的Nilpotent范式。通过引入一系列简单的变换和代数运算,而无需求解任何偏微分方程,即可得到高维非线性系统的Nilpotent范式。以四维非线性系统为例介绍这个方法。该方法完全适用于分析高于四维的非线性系统的Nilpotent范式。     

Synthesis of poly(Nε-phenoxycarbonyl-l-lysine) by polycondensation of activated urethane derivative and its application for selective modification of side chain with amines

We report a methodology for the synthesis of Nε-phenoxycarbonyl-protected poly(l -lysine) on the side chain by chain growth polycondensation of Nα,Nε-bis(phenoxycarbonyl)-l -lysine proceeded through the selective elimination of phenol and CO₂ from the Nα phenoxycarbonyl moiety at 50 °C in N,N-dimethylacetamide in the presence of a primary amine used as an initiator. After optimization of reaction condition, the addition of acetic acid during polycondensation proved effective for the realization of the predicted molecular weight and narrow dispersity of the corresponding polypeptide by adjusting the feed ratio of monomer to the amine initiator because of the suppression of interchain coupling that occurs between the amino terminus of poly(l -lysine) and the Nε-phenoxycarbonyl group on the polymer side chains. Furthermore, taking advantage of the potentially reactive Nε-phenoxycarbonyl moiety on the side chain, post-polymerization modification was effectively achieved by the nucleophilic reaction of amine compounds including primary, secondary, and aromatic amines through the formation of urea linkage, providing a useful platform for synthesis of selective side chain functionalization of poly(l -lysine) samples. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2522–2530     

A double Hopf bifurcation phenomenon

Summary A degenerate dynamic bifurcation phenomenon exhibited by autonomous systems is analyzed in detail. The situation arises when a key coefficient vanishes at a critical point where Hopf's transversality condition is also violated simultaneously. It is demostrated analytically that, unlike the phenomenon of Hopf bifurcation, in this case the existence of bifurcating family of limit cycles cannot be guaranteed. Indeed, an existence condition emerges as an integral part of the analysis. Under this existence condition, several topologically distinct phenomena may arise, and the conditions giving rise to such cases are discussed. the asymptotic equations of the bifurcating paths, the family of limit cycles and frequency-amplitude relationships are given in general, explicitforms which can be used in the analyses of specific problems directly.

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Sommario Il lavoro analizza in dettaglio un fenomeno di biforcazione dinamica degenere che si presenta in sistemi autonomi. La situazione sorge quando un coefficiente si annulla in un punto critico dove viene anche simultaneamente violata la condizione di trasversalità di Hopf. Si dimostra analiticamente che, a differenza del fenomeno di biforcazione alla Hopf, in questo caso l'esistenza di una famiglia biforcante di cicli-limite non può essere assicurata; infatti una condizione di esistenza emerge come parte integrante dell'analisi. Sotto tale condizione possono sorgere diversi fenomeni topologicamente distinti; si discutono le condizioni che danno luogo a questi casi. Le equazioni asintotiche degli itinerari di biforcazione, la famiglia di ciclilimite e le relazioni frequenza-ampiezza vengono fornite in forme generalied espliciteche possono essere usate direttamente nelle analisi di problemi specifici.

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The financial support of NSERC of Canada is acknowledged. A part of this paper was presented at 1984 IEEE Int. Sym. on Circuits and Systems, Montreal, Canada [1].     

The effect of symmetry on the imperfection-sensitivity of coincident critical points

Summary The imperfection sensitivity of an N-degree-of-freedom symmetric system exhibiting a two-fold coincident critical point is studied. Symmetry in one as well as in both the critical coordinates is considered. The concepts of general and special critical points, associated with smooth and improper equilibrium surfaces respectively, are used to explore all the relevant stability properties of the system without resorting to formal stability considerations. An illustrative example concerning a column on elastic foundation is analyzed.

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Übersicht Es wird die Parameter-Empfindlichkeit eines Systems von N Freiheitsgraden untersucht, das zwei zusammenfallende kritische Punkte besitzt. Dabei wird sowohl in einer als auch in beiden kritischen Koordinaten Symmetrie vorausgesetzt. Die Begriffe der allgemeinen und der speziellen kritischen Punkte, abgeleitet von den Eigenschaften der Gleichgewichtsoberflächen, werden dazu verwendet, alle wichtigen Stabilitätseigenschaften zu untersuchen, ohne daß die üblichen Stabilitätsbetrachtungen angestellt werden müssen. Als Beispiel wird eine Säule auf nachgiebiger Unterlage untersucht.

     

Highly sensitive octagonal photonic crystal fiber based sensor

In this study, a number of propagation characteristics of hexagonal and octagonal photonic crystal fiber (H-PCF and O-PCF) structures, where both core and cladding are microstructured have been investigated by employing the full vectorial finite element method (FEM). The confinement loss, the effective refractive index and the relative sensitivity coefficient behaviors of the O-PCF and the standard H-PCF are numerically investigated and compared. It is found that under the same design parameters O-PCF structure has significantly lower losses and higher relative sensitivity coefficient compared with H-PCF structure.     

New Amperometric Cholesterol Biosensors Using Poly(ethyleneoxide) Conducting Polymers

Accumulation of cholesterol in human blood can cause several health problems such as heart disease, coronary artery disease, arteriosclerosis, hypertension, cerebral thrombosis, etc. Therefore, simple and fast cholesterol determination in blood is clinically important. In this study, two types of amperometric cholesterol biosensors were designed by physically entrapping cholesterol oxidase in conducting polymers; thiophene capped poly(ethyleneoxide)/polypyrrole (PEO-co-PPy) and 3-methylthienyl methacrylate-co-p-vinyl benzyloxy poly(ethyleneoxide)/polypyrrole (CP-co-PPy). PEO-co-PPy and CP-co-PPy were synthesized electrochemically and cholesterol oxidase was immobilized by entrapment during electropolymerization. The amperometric responses of the enzyme electrodes were measured by monitoring oxidation current of H₂O₂ at +0.7 V in the absence of a mediator. Kinetic parameters, such as Km and Imax, operational and storage stabilities, effects of pH and temperature were determined for both entrapment supports. Km values were found as 1.47 and 5.16 mM for PEO-co-PPy and CP-co-PPy enzyme electrodes, respectively. By using these Km values, it can be observed that ChOx immobilized in PEO-co-PPy shows higher affinity towards the substrate.     

The effect of moisture content in fibre laser cutting of pine wood

This paper reports a statistical analysis of the multiple-pass laser cutting of wet and dry pine wood with a Ytterbium fibre laser. As multiple factors affect the laser wood cutting process, finding the optimal combination of process parameters is necessary to achieve good quality and high process efficiency. Design of experiments (DOE) and statistical modelling were used in this study to investigate the significant process parameters and their interactions. A high brightness, 1 kW IPG single mode, continuous wave Ytterbium doped fibre laser was employed to cut wet and dry pine wood samples. The parameters investigated are laser power, traverse speed, focal plane position (f.p.p.), gas pressure, number of passes, direction of cut (normal or parallel to wood's tracheids) and the moisture content. The experimental results were compared against process responses defining the efficiency (i.e. kerf depth and energy consumption) and quality of the cut section (i.e. kerf width, heat affected zone—HAZ, edge surface roughness and perpendicularity). It has been found that the laser cutting process was mainly affected by the moisture content and the cut direction with respect to the wood's tracheids, followed by traverse speed, laser power and the number of passes. The effect of moisture content on energy consumption in the laser cutting process of both wet and dry wood is analysed. The wood cutting results with fibre laser are compared with those from a CO₂ laser.