Pair Of Solutions Research Articles

A general chemical crosslinking strategy for structural analyses of weakly interacting proteins applied to preTCR–pMHC complexes

T lymphocytes discriminate between healthy and infected or cancerous cells via T-cell receptor-mediated recognition of peptides bound and presented by cell-surface-expressed major histocompatibility complex molecules (MHCs). Pre-T-cell receptors (preTCRs) on thymocytes foster development of αβT lymphocytes through their β chain interaction with MHC displaying self-peptides on thymic epithelia. The specific binding of a preTCR with a peptide–MHC complex (pMHC) has been identified previously as forming a weak affinity complex with a distinct interface from that of mature αβTCR. However, a lack of appropriate tools has limited prior efforts to investigate this unique interface. Here we designed a small-scale linkage screening protocol using bismaleimide linkers for determining residue-specific distance constraints between transiently interacting protein pairs in solution. Employing linkage distance restraint-guided molecular modeling, we report the oriented solution docking geometry of a preTCRβ–pMHC interaction. The linkage model of preTCRβ–pMHC complex was independently verified with paramagnetic pseudocontact chemical shift (PCS) NMR of the unlinked protein mixtures. Using linkage screens, we show that the preTCR binds with differing affinities to peptides presented by MHC in solution. Moreover, the C-terminal peptide segment is a key determinant in preTCR–pMHC recognition. We also describe the process for future large-scale production and purification of the linked constructs for NMR, X-ray crystallography, and single-molecule electron microscopy studies.

Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II

We consider the half-linear differential equation of the form \[ (p(t)|x^{\prime }|^{\alpha }\mathrm{sgn}\,x^{\prime })^{\prime } + q(t)|x|^{\alpha }\mathrm{sgn}\,x = 0\,, \quad t \ge t_{0} \,, \] under the assumption that $p(t)^{-1/\alpha }$ is integrable on $[t_{0}, \infty )$. It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as $t \rightarrow \infty $.

Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I

We consider the half-linear differential equation of the form \[(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},\] under the assumption \(\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty\). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as \(t \to \infty\).

Exp-function Method and Reduction Transformations for Rogue ‎Wave Solutions of the Davey-Stewartson Equations‎

A pair of rogue wave solutions of the Davey-Stewartson (DS) equations are obtained by using the exp-function method and reduction transformations. Firstly, the Davey-Stewartson equations are transformed into two easy-to-solve equations, one of which is the deformed nonlinear Schrodinger (NLS) equation and the other is a polynomial equation. Secondly, based on the existing known solutions of the deformed NLS equation constructed by the exp-function method, rogue wave solutions of the DS equations are obtained. Finally, some spatial and spatiotemporal structures and dynamical evolutionary plots of the obtained rogue wave solutions are shown.

Effect of Bjerrum pairs on the electrostatic properties of an electrolyte solution near charged surfaces: a mean-field approach.

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water molecules, on the electric double layer near charged surfaces. Based on the lattice statistical mechanics accounting for finite sizes and dipole moments of ions, Bjerrum pairs and solvent molecules, we consider the formation of Bjerrum pairs and derive the mathematical expressions for Bjerrum pair number density as well as cation/anion number density and water molecule number density. We reveal several significant phenomena. Firstly, it is shown that our approach naturally yields the equilibrium constant for dissociation-association equilibrium between Bjerrum pairs and ions. Secondly, at low surface charge densities, an increase in the bulk concentration of Bjerrum pairs enhances the permittivity and decreases the differential capacitance. Next, for the cases where Bjerrum pairs in an alcohol electrolyte solution have a high value of dipole moment, the Bjerrum pair number density increases with decreasing distance from the charged surface, and the differential capacitance and permittivity are high compared to those for the cases with lower values of Bjerrum-pair dipole moments. Finally, we show that the difference in the concentration and dipole moment of Bjerrum pairs can lead to some variation in osmotic pressure between two similarly charged surfaces.

EXISTENCE RESULTS FOR ANISOTROPIC FRACTIONAL (<i>p</i><sub>1</sub>(<i>x</i>, .), <i>p</i><sub>2</sub>(<i>x</i>, .))-KIRCHHOFF TYPE PROBLEMS

In this paper, we investigate the existence and multiplicity of solutions for a class of fractional $ (p_1(x,.),p_2(x,.)) $-Kirchhoff type problems with Dirichlet boundary data of the following form $ \left( \mathcal{P}_{M_i}^s\right) \; \; \left\{ \begin{array}{lllll} \sum\limits_{i = 1}^{2} M_i \left(\int_{Q}\frac{1}{p_i(x,y)}\frac{|u(x)-u(y)|^{p_i(x,y)}}{|x-y|^{N+sp_i(x,y)}}\; dxdy\right) \left( -\Delta\right)_{p_i(x,.)} ^{s}u(x)\\+\sum\limits_{i = 1}^{2}|u|^{\bar{p}_i(x)-2}u = f(x,u)\quad\rm{in}\; \; \Omega, u = 0 \quad \quad\rm{in}\; \; \; \mathbb{R}^{N}\setminus\Omega. \end{array}\right. $ More precisely, by means of mountain pass theorem with Cerami condition, we show that the above problem has at least one nontrivial solution. Moreover, using Fountain theorem, we prove that $ \left( \mathcal{P}_{M_i}^s\right) $ possesses infinitely many (pairs) of solutions with unbounded energy.

The Doubly Connected Minimal Surfaces Between Two Circles in Parallel Planes

In this article, we revisit some results published by several mathematicians regarding existence and non-existence of doubly connected minimal surfaces between two circles in parallel planes. In particular, we propose new analytical interpretations and results for catenoidal solutions formed between two coaxial circles in parallel planes of arbitrary radii. We conclude by discussing the nature of the pair of the catenoidal solutions that arise from our proposed algorithm.

Adsorption Kinetic and Isotherm of Solution Pair of Methylene Blue and Crystal Violet by Algae-Silica-Magnetite Hybrid Adsorbent on Porphyridium sp. Algae

Algae-silica-magnetite hybrid (PSM) from Porphyridium sp. algae has been successfully synthesized using precursor tetraethyl orthosilicate (TEOS) and coating with magnetite particles (Fe3O4) via a sol-gel process. The resulting adsorbent was applied for adsorption of solution pair of methylene blue (MB) and crystal violet (CV). The result of the analysis using the Infrared Spectrometer (IR) showed that in the PSM adsorbent there is an organic groups derived from Porphyridium sp. algae while silanol and siloxane group derived from silica matrix. In addition, surface morphology analysis results using Scanning Electron Microscopy With Energy Dispersive X-Ray (SEM-EDX) showed PSM surface has more heterogeneous than algae-silica hybrid (PS). The adsorption of solution pair of MB and CV by PSM was done under the experimental conditions of adsorbent of 0.1 g, interaction pH of 8, contact time of 90 min, and adsorbate concentration of 0.5 mmol L−1. The adsorption kinetics data indicate that it tends to follow the pseudo second order model with a correlation coefficient (R2) of 0.989 and 0.965 respectively. While, the adsorption isotherm model tends to follow Freundlich model.

Efficient Multi-Start With Path Relinking Search Strategy for Transmission System Expansion Planning

Transmission expansion planning is a complex problem that deals with the selection of new transmission lines that guarantee meeting future demand/generation and technical limits with the minimal investment cost. The transmission expansion planning problem has been solved through approaches and techniques aimed at reducing the computational effort required for its solution. Nevertheless, finding the optimal solution or even good-quality solutions for large-scale transmission systems is still challenging. In that context, an efficient multi-start with path relinking search strategy for the transmission expansion planning problem is proposed. The proposed strategy has two phases: constructive phase and local search. In the former, the multi-start applies a diversification process to guide the search along different regions to obtain good-quality solutions. Then, the local search phase executes an intensive search in the neighborhood of the best feasible solutions found in the constructive phase. The intensification process is performed in two steps: application of the Villasana-Garver-Salon algorithm in the best solutions after consecutive removal of transmission lines and path relinking using elite solution pairs. Tests performed using data from four systems show the efficiency of the proposed search strategy. Thus, the optimal solutions were obtained with a very low computational effort.

Absorption Refrigeration Systems Based on Ammonia as Refrigerant Using Different Absorbents: Review and Applications

The interest in employing absorption refrigeration systems is usually related to electricity’s precariousness since these systems generally use thermal rejects for their activation. The application of these systems is closely linked to the concept of energy polygeneration, in which the energy demand to operate them is reduced, which represents their main advantage over the conventional vapor compression system. Currently, the solution pairs used in commercial absorption chillers are lithium bromide/water and ammonia/water. The latter pair has been used in air conditioning and industrial processes due to the ammonia operation’s low temperature. Few review papers on absorption chillers have been published, discussing the use of solar energy as the input source of the systems, the evolution of the absorption refrigeration cycles over the last decades, and promising alternatives to increase the performance of absorption refrigeration systems. There is a lack of consistent studies about designing requirements for absorption chillers, so an updated review covering recent advances and suggested solutions to improve the use and operation of those absorption refrigeration systems using different working fluids is relevant. Hence, this presents a review of the state-of-the-art of ammonia/absorbent based absorption refrigeration systems, considering the most relevant studies, describing the development of this equipment over the years. The most relevant studies in the open literature were collected to describe this equipment’s development over the years, including thermodynamic properties, commercial manufacturers, experimental and numerical studies, and the prototypes designed and tested in this area. The manuscript focuses on reviewing studies in absorption refrigeration systems that use ammonia and absorbents, such as water, lithium nitrate, and lithium nitrate plus water. As a horizon to the future, the uses of absorption systems should be rising due to the increasing values of the electricity, and the environmental impact of the synthetic refrigerant fluids used in mechanical refrigeration equipment. In this context, the idea for a new configuration absorption chiller is to be more efficient, pollutant free to the environment, activated by a heat substantiable source, such as solar, with low cost and compactness structure to attend the thermal needs (comfort thermal) for residences, private and public buildings, and even the industrial and health building sector (thermal processes). To conclude, future recommendations are presented to deal with the improvement of the refrigeration absorption chiller by using solar energy, alternative fluids, multiple-effects, and advanced and hybrid configurations to reach the best absorption chiller to attend to the thermal needs of the residential and industrial sector around the world.

A mixed discontinuous Galerkin method for the wave equation

We study a mixed discontinuous Galerkin (DG) method for solving the second-order wave equation. The stress variable p and the displacement variable u are discretized by the mixed DG element pair Pk+1–Pk (k≥0). Under appropriate regularity assumptions on the solution pair, we derive optimal error estimates for the spatially semi-discrete scheme. Specifically, we prove the optimal convergence orders for u in L2 norm and p in L2 norm. Some test problems are presented, and the numerical results show that the orders of convergence coincide with the predicted error estimates.

A Proposed SUSY Alternative (SUSYA) Based on a New Type of Seesaw Mechanism Applicable to All Elementary Particles and Predicting a New Type of Aether Theory

This paper proposes a potentially viable “out-of-the-box” alternative (called “SUSYA”) to the currently known supersymmetry (SUSY) theory variants: SUSYA essentially proposes a new type of seesaw mechanism (SMEC) applicable to all elementary particles (EPs) and named “Z-SMEC”; Z-SMEC is a new type of charge-based mass symmetry/”conjugation” between EPs which predicts the zero/non-zero rest masses of all known/unknown EPs, EPs that are “conjugated” in boson-fermion pairs sharing the same electromagnetic charge (EMC). Z-SMEC is actually derived from an extended zero-energy hypothesis (eZEH) which is essentially a conservation principle applied on zero-energy (assigned to the ground state of vacuum) that mainly states a general quadratic equation governing a form of ex-nihilo creation and having a pair of conjugate boson-fermion mass solutions for each set of given coefficients. eZEH proposes a general formula for all the rest masses of all EPs from Standard model, also indicating the true existence of the graviton and a possible bijective connection between the three types of neutrinos (all predicted to be actually Majorana fermions) and the massless bosons (photon, gluon and the hypothetical graviton), between the electron/positron and the W boson, predicting at least three generations of leptoquarks (LQs) (defined here as the “mass-conjugates” of the three known generations of quarks) and predicting two distinct types of neutral massless fermions (NMFs) (modelled as mass-conjugates of the Higgs boson and Z boson respectively) which may be plausible constituents for a hypothetical lightest possible (hot fermionic) dark matter (LPDM) or, even more plausible, the main constituents of a superfluid fermionic vacuum/aether, as also proposed by the notorious Superfluid vacuum theory (SVT) (in which the physical vacuum is modeled as a bosonic/fermionic superfluid). SUSYA also predicts two hypothetical bosons defined as the ultra-heavy bosonic mass-conjugates of the muon and tauon called here the “W-muonic boson” (Wmb) and the “W-tauonic boson” (Wtb) respectively: Wmb and Wtb are predicted much heavier than the W boson and the Higgs boson so that Wmb and Wtb can be regarded as ultra-heavy charged Higgs bosons with their huge predicted rest energies defining the energy scale at which the electroweak field (EWF) may be unified with the Higgs field (HF).

FINITE ITERATIVE (R, S)-CONJUGATE SOLUTIONS OF THE GENERALIZED COMPLEX COUPLED SYLVESTER-TRANSPOSE EQUATIONS

The iterative method of generalized complex coupled Sylvester-transpose equations $ AXB+CY^TD = E,\; MX^TN+GYH = F $ over (R, S)-conjugate matrix solution $ (X,Y) $ is proposed. Usually, the type of matrix arises from some physical problems with some form of generalized reflexive symmetry. On the condition that the coupled matrix equations are consistent, we show the solution pair $ (X^*, Y^*) $ can be obtained by generalization of CG iterative method within finite iterative steps in the absence of roundoff-error for any initial guess chosen by the (R, S)-conjugate matrix. Moreover, the optimal approximation (R, S)-conjugate matrix solutions can be derived by searching the least Frobenius norm solution of the novel generalized complex coupled Sylvester-transpose matrix equations. Finally, some numerical examples are given to illustrate the presented iterative algorithm is efficient.

Decomposition-based co-evolutionary algorithm for interactive multiple objective optimization

We propose a novel co-evolutionary algorithm for interactive multiple objective optimization, named CIEMO/D. It aims at finding a region in the Pareto front that is highly relevant to the Decision Maker (DM). For this reason, CIEMO/D asks the DM, at regular intervals, to compare pairs of solutions from the current population and uses such preference information to bias the evolutionary search. Unlike the existing interactive evolutionary algorithms dealing with just a single population, CIEMO/D co-evolves a pool of subpopulations in a steady-state decomposition-based evolutionary framework. The evolution of each subpopulation is driven by the use of a different preference model. In this way, the algorithm explores various regions in the objective space, thus increasing the chances of finding DM’s most preferred solution. To improve the pace of the evolutionary search, CIEMO/D allows for the migration of solutions between different subpopulations. It also dynamically alters the subpopulations’ size based on compatibility between the incorporated preference models and the decision examples supplied by the DM. The extensive experimental evaluation reveals that CIEMO/D can successfully adjust to different DM’s decision policies. We also compare CIEMO/D with selected state-of-the-art interactive evolutionary hybrids that make use of the DM’s pairwise comparisons, demonstrating its high competitiveness.

Understanding Förster Energy Transfer through the Lens of Molecular Dynamics.

A multiscale approach to the dynamics of resonant energy transfer (RET) is presented, combining DFT and TD-DFT results on the energy donor (D) and acceptor (A) moieties with an extensive equilibrium and non-equilibrium molecular dynamics (MD) analysis of a bound D-A pair in solution to build a coarse-grained kinetic model. We demonstrate that a thorough MD study is needed to properly address RET: the enormous configuration space visited by the system cannot be reliably sampled accounting only for a few representative configurations. Moreover, the conformational motion of the RET pair, occurring in a similar time scale as the RET process itself, leads to a sizable increase of the overall process efficiency.

Spreading speed of the periodic Lotka-Volterra competition model

In this paper, we study the minimal speed (spreading speed) selection mechanism of traveling waves to a periodic diffusive Lotka-Volterra model with monostable nonlinearity. The method of upper and lower solutions pair is applied to establish the existence of traveling waves. We prove that the nature of nonlinear selection is to find a lower solution pair with the first species decaying in a faster rate. By novel constructions of various upper and lower solutions, we obtain a number of new results on the minimal speed determinacy. Numerical simulations are carried out to illustrate all of our discoveries.

Traveling wavefronts of a delayed temporally discrete reaction-diffusion equation

With the growth of a single species with age structure on an unbounded domain as a prototype, we derive a delayed temporally discrete reaction-diffusion equation. The main result is on the existence of traveling wavefronts of the equation. We first transform the problem into that on the existence of fixed points of a mapping. Then by successfully constructing a pair of upper and lower solutions, we establish the existence of traveling wavefronts by applying the upper-lower solution method.

Multiple Solution Results for Perturbed Fractional Differential Equations with Impulses

The multiplicity of classical solutions for impulsive fractional differential equations has been studied by many scholars. Using Morse theory, Brezis and Nirenberg’s Linking Theorem, and Clark theorem, we aim to solve this kind of problems. By this way, we obtain the existence of at least three classical solutions and k distinct pairs of classical solutions. Finally, an example is presented to illustrate the feasibility of the main results in this paper.

Boundary value problems associated with singular strongly nonlinear equations with functional terms

AbstractWe study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type(Φ(k(t)x′(t)))′+f(t,Gx(t))ρ(t,x′(t))=0,$$\big({\it \Phi}(k(t)\,x'(t))\big)' + f(t,{{\mathcal{G}}}_x(t))\,\rho(t, x'(t)) = 0,$$on a compact interval [a,b]. These equations are quite general due to the presence of a strictly increasing homeomorphismΦ, the so-calledΦ-Laplace operator, of a non-negative functionk, which may vanish on a set of null measure, and moreover of a functional term Gx. We look for solutions, in a suitable weak sense, which belong to the Sobolev spaceW1,1([a,b]). Under the assumptions of the existence of a well-ordered pair of upper and lower solutions and of a suitable Nagumo-type growth condition, we prove an existence result by means of fixed point arguments.

Theoretical Insights into Specific Ion Effects and Strong-Weak Acid-Base Rules for Ions in Solution: Deriving the Law of Matching Solvent Affinities from First Principles.

We present a detailed study of specific ion effects, volcano plots and the law of matching solvent affinities by means of a conceptual density functional theory (DFT) approach. Our results highlight that specific ion effects and the corresponding implications on the solvation energy are mainly due to differences in the electric chemical potentials and chemical hardnesses of the ions and the solvent. Our approach can be further used to identify reliable criteria for the validity of the law of matching solvent affinities. Basic expressions are derived, which allow us to study the limiting conditions for this empirical observation with regard to matching chemical reactivity indices. Moreover, we show that chaotropic and kosmotropic concepts and their implications for the stability of ion pairs are directly related to a generalized strong and weak acids and bases (SWAB) principle for ions in solution, which is also applicable to rationalize the shape of volcano plots for different solvents. In contrast to previous assumptions, all empirical findings can be explained by the properties of local solvent‐ion complexes which dominate the specific global behavior of ion pairs in solution.