Higher Derivatives Research Articles

Mixed orthogonality graphs for continuous‐time state space models and orthogonal projections

In this article, we derive (local) orthogonality graphs for the popular continuous‐time state space models, including in particular multivariate continuous‐time ARMA (MCARMA) processes. In these (local) orthogonality graphs, vertices represent the components of the process, directed edges between the vertices indicate causal influences and undirected edges indicate contemporaneous correlations between the component processes. We present sufficient criteria for state space models to satisfy the assumptions of Fasen‐Hartmann and Schenk (2024a) so that the (local) orthogonality graphs are well‐defined and various Markov properties hold. Both directed and undirected edges in these graphs are characterised by orthogonal projections on well‐defined linear spaces. To compute these orthogonal projections, we use the unique controller canonical form of a state space model, which exists under mild assumptions, to recover the input process from the output process. We are then able to derive some alternative representations of the output process and its highest derivative. Finally, we apply these representations to calculate the necessary orthogonal projections, which culminate in the characterisations of the edges in the (local) orthogonality graph. These characterisations are given by the parameters of the controller canonical form and the covariance matrix of the driving Lévy process.

Optimal decay of the Boltzmann equation

The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from the coupling structure between the transport operator and the linearized collision operator. Guo and Wang (Comm. Partial Differential Equations, 37, 2012) developed a general energy method for proving the optimal time decay rates of the solution to such type of equations in the whole space; however, the decay rate of the highest order spatial derivatives of the solution is not optimal. In this paper, by incorporating the high‐low frequency decomposition in the energy estimates, both linearly and nonlinearly, we prove the optimal decay rates of any high order spatial derivatives of the low frequency part of the solution to the Boltzmann equation and the almost exponential decay rate of the high frequency part, which imply in particular the optimal decay rate of the highest order spatial derivatives of the solution. Moreover, the velocity‐weighted assumption of the initial data required in Guo and Wang (Comm. Partial Differential Equations, 37, 2012) is removed by capturing the time‐weighted dissipation estimates via the time‐weighted energy method. The method can be applied to the compressible Navier–Stokes equations and many partially dissipative equations in kinetic theory and fluid dynamics.

Second law and Liu relations: the no-reversible-direction axiom—revisited

AbstractA thermodynamic process is governed by balance equations in field-formulated thermodynamics. Especially the balance equation of entropy takes a prominent role: it introduces the Second Law in the form of a dissipation inequality via the non-negative entropy production. Balance equations and dissipation inequality are independent of the considered material which is described by additional constitutive equations which need the introduction of a state space which is spanned by the state space variables. Inserting these constitutive equations into the balance equations results in the balance equations on state space which include the first order time and position derivatives of the state space variables, called “higher derivatives” wich are directional derivatives in a mathematicle sense. Why do not appear the latter in the Liu Relations which pretend to describe material as well as the equations on state space do ? The answer is that the Liu Relations describe materials whose entropy production does not depend on the higher derivatives. Consequently, the Liu Relations are more specific than the balance equations on state space. A toy example concerning heat conduction in compressible fluids is in two different versions added for elucidation.

Matrix analysis of discrete functionals in compact difference method for nonlinear problems with higher derivatives and program code (I: 1D problem)

Matrix analysis of discrete functionals in compact difference method for nonlinear problems with higher derivatives and program code (I: 1D problem)

Complete CP-eigen bases of meson-baryon chiral lagrangian up to p5-order

Chiral perturbation theory describes the low energy dynamics of mesons and baryons in terms of the nonlinear Goldstone boson and fermion degrees of freedom. Through the Young tensor technique, we construct the on-shell operator bases for the meson-baryon system up to p5-order, using the chiral dimension power counting and heavy baryon expansion. For the Lorentz structure, additional treatments on off-shell external sources and operators with higher derivatives are necessarily considered, while for the internal structure, the invariant tensor basis is converted into the trace basis equivalently, and Cayley-Hamilton relations are utilized to classify different CP eigen-operators. Finally we present the complete operator set of C+P+, C+P-, C-P+, and C-P- eigen-operators at the p5-order, and obtain the operator counting from the Hilbert series.

Reducing Leakage of Single-Qubit Gates for Superconducting Quantum Processors Using Analytical Control Pulse Envelopes

Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the ef transition of a transmon qubit with an anharmonicity of −212 MHz, we implement RX(π/2) gates achieving a leakage error below 3.0×10−5 down to a gate duration of 6.25 ns without the need for iterative closed-loop optimization. The obtained leakage error represents a 20-fold reduction in leakage compared to a conventional cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of (1.56±0.07)×10−4 at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control-pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion. Published by the American Physical Society 2024

Variational consistent one-point integration with Taylor's expansion-based stabilization in the second-order meshfree Galerkin method for strain gradient elasticity

A generalized variational principle with five independent variables is proposed for strain gradient elasticity, including displacement, strain, strain gradient, stress, and double stress. Based on the principle, a one-point integration scheme is designed for the second order meshfree Galerkin method through nodal smoothed derivatives and their high order derivatives by Taylor's expansion. Since the proposed integration scheme meets the orthogonality conditions, it is variational consistent. The weak form expanded with Taylor's polynomials can be well evaluated by nodal smoothed derivatives and their high order derivatives on one quadrature point. Numerical one- and two-dimensional case studies show that the proposed integration scheme performs better than the standard Gaussian integration method in terms of accuracy, convergence, efficiency, and stability.

TsOH-catalyzed dehydroxylative cross-coupling of alcohols with phenols: rapid access to propofol derivatives.

Modification of the parent structure of molecules often alters their physicochemical properties and biological activities. Herein, a practical, efficient, and highly regioselective C-H alkylation of phenols with alcohols via dehydroxylative cross-coupling was developed to produce para-alkylated phenols with excellent regioselectivities and yields, using which propofol derivatives were rapidly synthesized. This process is performed under mild and simple conditions and is well-compatible with a variety of alcohols (secondary and tertiary benzylic alcohols as well as allyl alcohols) as alkylated agents. In addition, high aryl ether derivatives were also obtained using this catalytic system.

Optimization of synthesis method for carboxymethylcellulose (CMC) from agro-food wastes by response surface methodology (RSM) using D-Optimal algorithm

Carboxymethylcellulose (CMC) has wide commercial applicability for oil drilling fluids, cosmetics, food, and pharmaceutical industries, but the current industrial process for its synthesis from eucalyptus wood has low sustainability and efficiency. This work reports the statistical optimization for the synthesis of CMC from waste biomass celluloses with special reactivity, extracted from sugarcane bagasse (SB) and corn cob (CC). The combined mild acid/peroxide-alkali (APA) treatment, followed by bleaching, was efficient for the extraction of low-crystallinity pulps, which were further converted into CMC. A set of carboxymethylation tests with variable reaction conditions determined by a D-Optimal design of experiments (DoE) were carried out by assessing the factors Activation Time (AT), Reaction Time (RT), NaOH concentration (NaOH%) and Cellulose (SBCel or CCel). Characteristic CMC absorption features were observed via FTIR and Raman spectra, and the deconvolution of X-ray diffractograms showed that the mild APA treatment is able to produce pulps with significant content of amorphous and type II celluloses, whose have higher reactivity and reflects in the optimal results of the DoE. Analysis of variance (ANOVA) and response surface methodology (RSM) results from DoE data proved with high precision (F=184.81; p-value<0.0001; R2=0.9911; SD<1.0×10–5) and accuracy (low regression residuals) that the waste celluloses extracted are promising to produce CMC under milder conditions in comparison to literature, yielding up to 227 % (w CMC/w cellulose) of water-soluble CMC at lower AT and RT. The optimized process is more sustainable, low-cost, and efficient for producing this high valued-added cellulose derivative in the concept of biorefinery.

Asymptotics of the Solution of a Two-Point Bundary-Value Problem with Single Points

In many areas of science, complex problems are described by differential equations with a small parameter. One famous physicist is credited with the phrase: A phenomenon is not physical if it lacks a small parameter. A differential equation (ordinary or partial differential) with a small parameter at the highest derivative is called a singularly perturbed differential equation. Such equations arise in electrical and radio engineering, mechanics, hydraulic and aerodynamics, etc. The article is devoted to the construction of a complete expansion of the solution to a singularly perturbed two-point boundary value problem with two singular points on the boundaries of the segment under consideration. The solution is sought in the form of a sum of three functions that can be represented by asymptotic series. It is impossible to construct a uniform asymptotic expansion on a straight line, so an auxiliary function is introduced, with the help of which it is possible to construct an asymptotic expansion on the entire segment, including singular points.

High Energy Density Asymmetric Tetrathiafulvalene Derivative as a Catholyte for Non-Aqueous Redox Flow Batteries

The inherent intermittency challenge associated with renewable energy sources prompts the rapid development of cost-effective, grid-scale energy storage technologies. Redox flow batteries (RFBs) represent a promising solution to this problem owing to their remarkable potential for scalability and the tunability offered by a wide range of available solution-based chemistries. However, to-date, RFB commercialization has been challenged by a lack of long-lived, energy-dense, and earth abundant charge storage materials. Many of these challenges can be addressed with the development of non-aqueous organic redox flow batteries (NAORFBs). Such batteries leverage the wide potential window (> 5.5 V) offered by organic solvents with the synthetic tunability of organic redox cores to create highly energy dense battery systems with electrolytes based on earth abundant materials (i.e., carbon, nitrogen, sulfur, oxygen, etc.). The energy density of NAORFBs can be optimized with strategies such as increasing the solubility of redoxmers, increasing the number of electrons transferred by redoxmers, and increasing the magnitude of the potential of employed redox materials [1]. Of these, solubility can be enhanced through the grafting of polar side groups to a redoxmer, while redox potential can be increased through the attachment of either electron-withdrawing or donating substituents, in the case of catholyte and anolytes, respectively, near or in conjugation with the redox core [2]. Recently, our group has demonstrated tetrathiafulvalene (TTF) as a robust, two-electron active catholyte material in NAORFBs [3]. Namely, TTF exhibits reversible oxidation events at 0.03 and 0.43 V vs. Ag/Ag+ (Figure 1A). Underivatized TTF, which is highly insoluble in many polar organic solvents, can be made miscible in MeCN, carbonates, and ethereal solvents, with the attachment of four PEG3 chains to the TTF core ((PEG3)2-TTF) (Figure 1B). When paired with a low potential Li metal anode, an RFB incorporating 0.5 M (PEG3)2-TTF (1.0 M e- concentration) in 1.0 M LiPF6-EC/EMC supporting electrolyte exhibits overall operating cell potentials of 3.44 and 3.64 V vs. Ag/Ag+. Here we describe our most recent efforts to develop a further optimized, rationally designed asymmetric TTF derivative – (PEG3/PerF)-TTF – incorporating both a perfluorophenyl ring fused directly to the TTF core and two PEG3 side chains (Figure 1B). The electron-withdrawing perfluorophenyl group functions to substantially raise the potential of both redox events to 0.43 V and 0.65 V vs. Ag/Ag+, while the two PEG3 chains allow the material to retain miscibility in polar solvents. The performance of (PEG3/PerF)-TTF has been successfully demonstrated in a battery at an even higher concentration of 0.75 M (1.5 M e- concentration) (Figure 1C). When also paired with a Li metal anode in 1.0 M LiPF6-EC/EMC supporting electrolyte, the battery exhibits exceptional operational energy density of 96 Wh/L at 6 mA/cm2 current density and capacity retention of 83.1% over 16.8 d of continuous operation (99.0% per d). These results further demonstrate TTF as a highly versatile catholyte with remarkable potential for application in NAORFBs.

Consistent actions for massive particles interacting with electromagnetism and gravity

Consistent interactions with electromagnetism and gravity for mass m particles of any spin are obtained. This is done by finding interactions which preserve the covariantized massive gauge symmetry present in recently constructed massive particle actions. This gauge principle is sufficient for finding consistent completions of minimal as well as non-minimal couplings of any type. For spins s ≥ 3/2, consistency requires infinitely many interaction terms in the action, including arbitrarily high order derivatives of electromagnetic and gravitational curvatures, with correspondingly high powers of 1/m. These interactions may be formally resummed and expressed in terms of non-local operators. Finally, although the interactions appear non-local, evidence is presented for the existence of a field redefinition which makes the interacting action local. This work provides the first explicit realization of an exactly gauge invariant formulation of massive particles interacting with electromagnetism and gravity.

Effectiveness of Weyl gravity in probing quantum corrections to AdS black holes

Computing leading higher curvature contributions to thermodynamic quantities of AdS black hole is drastically simplified once the higher curvature terms are expressed in terms of powers of Weyl tensor by applying proper field redefinitions, avoiding the usual complications caused by higher derivative Gibbons-Hawking-York term or surface counterterms. We establish the method by computing the Euclidean action of general rotating anti–de Sitter (AdS) black holes in five-dimensional quadratic curvature theories with or without supersymmetry and verifying the results numerically. Our result is the state of the art for charged rotating AdS black holes in five-dimensional minimal gauged supergravity including corrections from all three supersymmetric curvature squared terms. Our approach facilitates precision tests in the AdS/CFT correspondence and should be applicable in diverse dimensions. Published by the American Physical Society 2024

Asymptotical convergence of solutions of boundary value problems for singularly perturbed higher-order integro-differential equations

The article considers a two-point boundary value problem for a linear integro-differential equation of the n + m order with small parameters for m higher derivatives, provided that the roots of the additional characteristic equation are negative. The aim of the study is to obtain asymptotic estimates of the solution, to find out the asymptotic behavior of solutions in the vicinity of points where additional conditions are set, as well as to construct a degenerate problem, the solution of which tend to the solution of the initial perturbed boundary value problem. The Cauchy function and boundary functions of a boundary value problem for a singularly perturbed homogeneous differential equation are constructed, and their asymptotic estimates are obtained. Using the Cauchy functions and boundary functions, an analytical formula for solutions to the boundary value problem is obtained. A theorem on an asymptotic estimate for the solution of the considered boundary value problem is proved. The asymptotic behavior of the solution with respect to a small parameter and the order of growth of its derivatives are established. It is shown that the solution of the boundary value problem under consideration at the left end of this segment has the phenomenon of an initial jump and the order of this jump is determined. A modified degenerate boundary value problem containing initial jumps of the solution and the integral term is constructed.

Approximation of time separating stochastic processes by neural networks revisited

Here we study the univariate quantitative approximation of time separating stochastic process over the whole real line by the normalized bell and squashing type neural network operators. Activation functions here are of compact support. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged stochastic function or its high order derivative. The approximations are pointwise and with respect to the Lp norm. The feed-forward neural networks are with one hidden layer. We finish with a great variety of special applications.

Exploring novel dilazep derivatives as hENT1 inhibitors and potentially covalent molecular tools.

The human equilibrative nucleoside transporter 1 (SLC29A1, hENT1) is a solute carrier that modulates the passive transport of nucleosides and nucleobases, such as adenosine. This nucleoside regulates various physiological processes, such as vasodilation and -constriction, neurotransmission and immune defense. Marketed drugs such as dilazep and dipyridamole have proven useful in cardiovascular afflictions, but the application of hENT1 inhibitors can be beneficial in a number of other diseases. In this study, 39 derivatives of dilazep's close analogue ST7092 were designed, synthesized and subsequently assessed using [3H]NBTI displacement assays and molecular docking. Different substitution patterns of the trimethoxy benzoates of ST7092 reduced interactions within the binding pocket, resulting in diminished hENT1 affinity. Conversely, [3H]NBTI displacement by potentially covalent compounds 14b, 14c, and 14d resulted in high affinities (Ki values between 1.1 and 17.5 nM) for the transporter, primarily by the ability of accommodating the inhibitors in various ways in the binding pocket. However, any indication of covalent binding with amino acid residue C439 remained absent, conceivably as a result of decreased nucleophilic residue reactivity. In conclusion, this research introduces novel dilazep derivatives that are active as hENT1 inhibitors, along with the first high affinity dilazep derivatives equipped with an electrophilic warhead. These findings will aid the rational and structure-based development of novel hENT1 inhibitors and pharmacological tools to study hENT1's function, binding mechanisms, and its relevance in (patho)physiological conditions.

Cytological structures and physiological and biochemical characteristics of covered oat (Avena sativa L.) and naked oat (Avena nuda L.) seeds during high-temperature artificial aging

BackgroundSeed aging, a natural and inevitable process occurring during storage. Oats, an annual herb belonging to the Gramineae family and pooideae. In addition to being a healthy food, oats serve as ecological pastures, combating soil salinization and desertification. They also play a role in promoting grassland agriculture and supplementing winter livestock feed. However, the high lipid and fat derivatives contents of oat seeds make them susceptible to deterioration, as fat derivatives are prone to rancidity, affecting oat seed production, storage, development, and germplasm resource utilization. Comparative studies on the effects of aging on physiology and cytological structure in covered and naked oat seeds are limited. Thus, our study aimed to determine the mechanism underlying seed deterioration in artificially aged ‘LongYan No. 3’ (A. sativa) and ‘BaiYan No. 2’ (A. nuda) seeds, providing a basis for the physiological evaluation of oat seed aging and serving as a reference for scientifically safe storage and efficient utilization of oats.ResultsIn both oat varieties, superoxide dismutase and catalase activities in seeds showed increasing and decreasing trends, respectively. Variance analysis revealed significant differences and interaction in all measured indicators of oat seeds between the two varieties at different aging times. ‘LongYan No. 3’ seeds, aged for 24–96 h, exhibited a germination rate of < 30%, Conductivity, malondialdehyde, soluble sugar, and soluble protein levels increased more significantly than the ‘BaiYan No. 2’. With prolonged aging leading to cell membrane degradation, reactive oxygen species accumulation, disrupted antioxidant enzyme system, evident embryo cell swelling, and disordered cell arrangement, blocking the nutrient supply route. Simultaneously, severely concentrated chromatin in the nucleus, damaged mitochondrial structure, and impaired energy metabolism were noted, resulting in the loss of ‘LongYan No. 3’ seed vitality and value. Conversely, ‘BaiYan No. 2’ seeds showed a germination rate of 73.33% after 96 h of aging, consistently higher antioxidant enzyme activity during aging, normal embryonic cell shape, and existence of the endoplasmic reticulum.ConclusionsROS accumulation and antioxidant enzyme system damage in aged oat seeds, nuclear chromatin condensation, mitochondrial structure damage, nucleic acid metabolism and respiration weakened, oat seed vigor decreased. ‘LongYan No. 3’ seeds were more severely damaged under artificial aging than ‘BaiYan No. 2’ seeds, highlighting their heightened susceptibility to aging effects.

Ghost problem, spectrum identities and various constraints on brane-localized gravity

This paper investigates the brane-localized interactions, including DGP gravity and higher derivative (HD) gravity localized on the brane. We derive the effective action on the brane, which suggests the brane-localized HD gravity suffers the ghost problem generally. Besides, we obtain novel algebraic identities of the mass spectrum, which reveal the global nature and can characterize the phase transformation of the mass spectrum. We get a powerful ghost-free condition from the spectrum identities, which rules out one type of brane-localized HD gravity. We further prove the mass spectrum is real and non-negative m2 ≥ 0 under the ghost-free condition.Furthermore, we discuss various constraints on parameters of brane-localized gravity in AdS/BCFT and wedge holography, respectively. They include the ghost-free condition of Kaluza-Klein and brane-bending modes, the positive definiteness of boundary central charges, and entanglement entropy. The ghost-free condition imposes strict constraint, which requires non-negative couplings for pure DGP gravity and Gauss-Bonnet gravity on the brane. It also rules out one class of brane-localized HD gravity. Thus, such HD gravity should be understood as a low-energy effective theory on the brane under the ghost energy scale. Finally, we briefly discuss the applications of our results.

Design and Study of Simple Biogas Reactor using Kitchen Waste Within the Habitat of Federal Polytechnic of Oil and Gas Bonny Island, Rivers State, Nigeria

This research work is about design and study of simple biogas reactor using Kitchen Waste within the habitat of Federal Polytechnic of Oil and Gas Bonny Island, Rivers State, Nigeria to produce gas. The objective of the work is to collect and measure the amount of waste that is been generated within the study area as well as to construct a simple laboratory scale biogas reactor and using the kitchen waste as substrate and measure the amount of gas that is been generated from biogas reactor per day. Based on the objective for this research a biogas digester was designed. Two experiments was carried out to determine the extent of production of biogas and the duration required so as to determine the rate of formation of biogas. In experiment one, dissimilar kinds of biomass like rice, potato, green leaves, sugar in different amounts were mixed with cow dung and rice husk to prepare 4 samples to determine the maximum generation of biogas through fermentation process. The gas is collected in balloons and they were measured to determine the amount of gas produced in each sample. The extent to which the blowing of balloons took place determined the quantity of gas evolved in each of the incumbent samples. In experiment two, we have used two 5lt. bottles in which the amount of cow dung used varies while same amount of kitchen waste mixture was utilized. The process and conditions for trapping and analyzing the gas is the same as in experiment one. From this experiment the rapidness of formation of biogas was observed. The experimental analysis carried out also gives us a clear idea of the indulgence of materials with respect to their combination to deferring extent of concentration to deliver optimum generation of biogas, in particular methane thereby unveiling us to develop an imminent and high performance derivative affordable biogas reactor.

Deriving interaction vertices in higher derivative theories

We derive cubic interaction vertices for a class of higher-derivative theories involving three arbitrary integer spin fields. This derivation uses the requirement of closure of the Poincaré algebra in four-dimensional flat spacetime. We find two varieties of permitted structures at the cubic level and eliminate one variety, which is proportional to the equations of motion, using suitable field redefinitions. We then consider soft theorems for field theories with these higher-derivative interactions and construct amplitudes in these theories using the inverse-soft approach.