Form Of Solution Research Articles

Fluorescent Artificial Receptor for Dopamine based on Molecular Recognition-driven Dynamic Covalent Chemistry in a Lipid Nanoreactor.

Molecular recognition and detection of small bioactive molecules, like neurotransmitters, remain a challenge for chemists, whereas nature found an elegant solution in form of protein receptors. Here, we introduce a concept of a dynamic artificial receptor that synergically combines molecular recognition with dynamic imine bond formation inside a lipid nanoreactor, inducing a fluorescence response. The designed supramolecular system combines a lipophilic recognition ligand derived from a boronic acid, a fluorescent aldehyde based on push-pull styryl pyridine and a phenol-based catalyst. The recognition ligand specifically captures dopamine inside lipid nanodroplets and thus triggers imine bond formation with the aldehyde, producing the emission color change. The rational design of the fluorescent aldehyde, the catalyst and the recognition ligand allows dramatic acceleration of the imine bond formation required for rapid sensing of dopamine. The nanoprobe enables dopamine detection with micromolar sensitivity and singe-nanoprobe imaging of dopamine gradients through its robust two-color ratiometric response. It displays remarkable selectivity without interference of competing biogenic primary amines and biological media: blood serum, plasma, urine and cell lysate. The proposed concept of a dynamic artificial receptor offers a solution to the long-standing problem of molecular recognition and sensing of small molecules in complex biological media.

Fluorescent Artificial Receptor for Dopamine based on Molecular Recognition‐driven Dynamic Covalent Chemistry in a Lipid Nanoreactor

Molecular recognition and detection of small bioactive molecules, like neurotransmitters, remain a challenge for chemists, whereas nature found an elegant solution in form of protein receptors. Here, we introduce a concept of a dynamic artificial receptor that synergically combines molecular recognition with dynamic imine bond formation inside a lipid nanoreactor, inducing a fluorescence response. The designed supramolecular system combines a lipophilic recognition ligand derived from a boronic acid, a fluorescent aldehyde based on push‐pull styryl pyridine and a phenol‐based catalyst. The recognition ligand specifically captures dopamine inside lipid nanodroplets and thus triggers imine bond formation with the aldehyde, producing the emission color change. The rational design of the fluorescent aldehyde, the catalyst and the recognition ligand allows dramatic acceleration of the imine bond formation required for rapid sensing of dopamine. The nanoprobe enables dopamine detection with micromolar sensitivity and singe‐nanoprobe imaging of dopamine gradients through its robust two‐color ratiometric response. It displays remarkable selectivity without interference of competing biogenic primary amines and biological media: blood serum, plasma, urine and cell lysate. The proposed concept of a dynamic artificial receptor offers a solution to the long‐standing problem of molecular recognition and sensing of small molecules in complex biological media.

Technology Adoption and Organizational Change

Technology and the use of digital platforms can be seen as being key for traditional sectors in a bid to survive the ever growingtrend of technological difference. This paper analyses Dangote Company, a leading industrial conglomerate in Nigeria, to understand the challenges of digital transformation. By evaluating the current technological developments and their relation to the subject of investigation, the study points out the critical importance of digital solutions in forms of contemporary organizational development, capability development and sustainable improvement. This evidence has emphasized that technology training and technology literacy are essential to help in issues with the implementation of tactics and championing of innovation culture for sustainable development in the traditional sectors. Consequently, this paper to the existing body of knowledge on digital transformation in emerging markets, and provides specific guidance and advice that other industries can adapt to their own digital transformation initiatives.

ALGORITHMIC DIFFERENCES OF COMPLETE AND PARTIAL ALGEBRAIC SYNTHESIS OF A FINITE STATE MACHINE WITH DATAPATH OF TRANSITIONS

Context. The problem of algorithmization the search for formal solutions of the problem of algebraic synthesis of a finite state ma-chine with datapath of transitions is considered. The concept of complete and partial solutions of this problem is proposed. The object of research is the automated synthesis of the finite state machine in the part of the function of transitions without taking into account the function of outputs. The basis of the algebraic implementation of the transition function is the author's approach to the transformation of state codes using a set of arithmetic and logical operations. The search for formal solutions to the problem of algebraic synthesis is a complex process that requires the use of appropriate methods and algorithms aimed at special coding of states and mapping of operations of transitions to individual state machine transitions. The use of partial solutions of the problem of algebraic synthesis can contribute to reducing the executing time of such algorithms and reducing the overall design time of digital control devices based on a finite state machine with an datapath of transitions. Objective. Development and research of algorithms for finding complete and partial solutions to the problem of algebraic synthesis of a finite state machine with datapath of transitions. Method. The research is based on the structure of a finite state machine with datapath of transitions. The synthesis of the circuit of the state machine involves the preliminary solution of the problem of algebraic synthesis. The result is the so-called formal solution of this problem, which contains two components. The first component is defined state codes, the second component is arithmetic and logic operations mapped to separate state machine transitions. Finite state machine can be synthesized in that case if transformation of given state codes in the process of making transitions is possible using a given set of operations. Verification of this possibility is carried out using the known matrix approach. It involves the formation and element-by-element mapping of two matrices – the matrix of transitions and the combined matrix of operations. As a result, a coverage matrix is formed, which reflects the possibility of implementing (covering) of state machine transitions by specified arithmetic and logic operations. Changing the way of encoding states or the set of operations can give different solutions to the problem of algebraic synthesis with a greater or lesser number of covered state machine transitions. Results. Using the example of an abstract graph-scheme of the control algorithm, it is demonstrated that the solution of the problem of algebraic synthesis of a finite state machine with datapath of transitions can be considered a situation when one or more state machine transitions cannot be implemented using a given set of operations. It is proposed to call such situation as a partial solution of the problem of algebraic synthesis. The implementation of all transitions by specified operations gives a complete solution of this problem, but the number of complete solutions is always much smaller than the number of partial solutions. Therefore, in the general case, the search for complete solutions takes much more time and, moreover, is not always possible. Conclusions. The design of a logical circuit of a finite state machine with datapath of transitions is possible in the case of a complete or partial solution of the problem of algebraic synthesis. In the case of a partial solution, those transitions that cannot be implemented by any of the available operations are implemented in a canonical way using a system of Boolean equations. The search for complete solutions generally takes more time than the search for partial solutions. This makes actual the development of algorithms and methods of synthesis of this class of finite state machine, based on the search for partial solutions of the problem of algebraic synthesis.

Results on left–right Artin approximation for algebraic morphisms and for analytic morphisms of weakly‐finite singularity type

AbstractThe classical Artin approximation (AP) reads: any formal solution of a system of (analytic, resp., algebraic) equations of implicit function type is approximated by “ordinary” solutions (i.e., analytic, resp., algebraic). Morphisms of scheme‐germs, for example, , are usually studied up to the left–right equivalence. The natural question is the left–right version of AP: when is the formal left–right equivalence of morphisms approximated by the “ordinary” (i.e., analytic, resp., algebraic) equivalence? In this case, the standard AP is not directly applicable, as the involved (functional) equations are not of implicit function type. Moreover, the naive extension does not hold in the analytic case, because of Osgood–Gabrielov–Shiota examples. The left–right version of Artin approximation (.AP) was established by M. Shiota for morphisms that are either Nash or [real‐analytic and of finite singularity type]. We establish .AP and its stronger version of Płoski (.APP) for , where are analytic/algebraic germs of schemes of any characteristic. More precisely: .AP, .APP, the inverse AP (and its Płoski's version) hold for algebraic morphisms and for finite analytic morphisms; .AP holds for analytic morphisms of weakly‐finite singularity type. (For we impose certain integrability condition.) This latter class of morphisms of “weakly‐finite singularity type” (which we introduce) is of separate importance. It extends naturally the traditional class of morphisms of “finite singularity type,” while preserving their nonpathological behavior. The definition goes via the higher critical loci and higher discriminants of morphisms with singular targets. We establish basic properties of these critical loci. In particular, any map is finitely (right) determined by its higher critical loci.

Francesco Placidi and Ludwig Ladislaus. On architect and sculptor partnership in the 1740s and 1750s

Two artists, Francesco Placidi from Rome and sculptor Ludwig Ladislaus from Opava, played a significant role in Krakow artistic circles of the 1740s and 1750s. Placidi was brought to Poland by another Roman architect, Gaetano Chiaveri, under whose guidance he directed the construction of the court church in Dresden, and was active in Kraków since 1742. Ladisalus was first recorded in the records of the city of Krakow in 1741. The two lived in the same parishes, first All Saints’ and then St Mary’s, and were connected both socially and professionally. Following the study of sources and styles, it was determined that Placidi designed and Ladilaus executed the interior furnishings of the parish church in Morawica (c. 1748–55) funded by Aleksander August and Maria Zofia Czartoryski, the main altar in the Sanctuary of the Crucified Christ in Kobylanka (c. 1750) funded by Jan Wielopolski, and the main altar in the former collegiate church in Sandomierz (1756–57). A detailed investigation outlined the origin of architectural solutions defined by Placidi and captured the stylistic and formal features that Ladislaus’s sculptures share. The case is but a contribution to further research on the mutual relations between designers and makers of architecture and sculptures. Especially with respect to the roles of both the Italian architect imposing (or not) the general and/or detailed concept of the work, and the sculptor following (or not) the designer’s ideas, yet also contributing his own formal and stylistic solutions resulting from his individual artistic path of development (in the case of Ladislaus: in the Austrian Silesia). Beyond doubt, with his extensive contacts with ecclesiastical and secular aristocracy and the royal court, Placidi played an important role in Kraków, providing a link between artists of various professions, and maintaining familial and social contacts with some.

Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity

Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity

Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces

We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-0 fields (solutions to the wave equation) on n-dimensional Minkowski spacetimes in a neighbourhood of spatial and null infinity. We obtain formal solutions written in terms of series expansions close to spatial and null infinity and use them to compute non-trivial asymptotic spin-0 charges. It is shown that if one examines the most general initial data within the class considered in this paper, the expansion is polyhomogeneous and hence of restricted regularity at null infinity. Furthermore, we derive the conditions on the initial data needed to obtain well-defined limits for the asymptotic charges at the critical sets where null infinity and spatial infinity meet. In four dimensions, we find that there are infinitely many well-defined asymptotic charges at the critical sets, while for higher dimensions there is only a finite number of non-trivial asymptotic charges with well-defined limits at the critical sets.

On the existence and convergence of formal power series solutions of nonlinear Mahler equations

As known, any formal power series solution φ∈C[[x]] of an algebraic equation is convergent, as well as that of an analytic one. We study the convergence of formal power series solutions of Mahler functional equations F(x,y(x),y(xℓ),…,y(xℓn))=0, where ℓ⩾2 is an integer and F is a holomorphic function near 0∈Cn+2. Extending Bézivin's theorem from the polynomial case to the case under consideration we prove that all such solutions are also convergent. The Newton polygonal method for finding them is explained.

Formal solutions of some family of inhomogeneous nonlinear partial differential equations, Part 2: Summability

In this article, we investigate the summability of the formal power series solutions in time of a class of inhomogeneous nonlinear partial differential equations in two variables, whose corresponding Newton polygon admits a unique positive slope k, the latter being determined by the highest spatial-derivative order of the initial equation. We give in particular a necessary and sufficient condition for the k-summability of the solutions in a given direction, and we illustrate this result by some examples. This condition generalizes the ones already given by the second author in Remy (2016, 2020, 2021 [25,26], 2022, 2023). In addition, we present some technical results on the generalized binomial and multinomial coefficients, which are needed for the proof of our main result.

Environmental and architectural aspects of wooden construction: a comparative analysis of selected issues of single-family housing in Poland and Portugal

In the second half of the 20th century, it seemed that wooden architecture would be replaced by other, increasingly used, technologies. Wood was primarily used in hybrid systems, rather than as the dominant construction and finishing material. However, the turn of the 20th and 21st centuries reversed this trend. There is now a growing interest in wooden structures and finishes. Wood is becoming a “fashionable” material. This shift is influenced by new technologies that provide innovative construction possibilities, as well as by new methods of protecting wood. Wood is a renewable, ecological material with a small built-in carbon footprint, making it easy to recycle and suitable for a circular economy. The aim of the study is to compare the features of wooden single-family houses in Poland and Portugal. The methods necessary for this purpose were employed: critical analysis, observation without intervention and case studies to compare contemporary architectural trends. The results of research on current trends in shaping wooden single-family architecture allowed for drawing conclusions regarding formal, functional and pro-environmental solutions.

Algebraic Complete Integrability of the $a_4^{(2)}$ Toda Lattice

The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this system is an affine part of an abelian surface. Second, we show that the flows of integrable vector fields on this surface are linear. Finally, using the formal Laurent solutions of the system, we provide a detailed geometric description of these abelian surfaces and the divisor at infinity.

Q-Nagumo norms and formal solutions to singularly perturbed q-difference equations

q-Nagumo norms and formal solutions to singularly perturbed q-difference equations

Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series

We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel–Padé approximant and classical analysis to determine the analytic structure of the solution using the first few terms of its asymptotic series. Afterward, we build an approximant, consistent with the resurgent properties of the equation. The procedure gives an approximate expression for the Borel–Ecalle resummation of the solution useful for practical applications. Connections with other physical applications are also discussed.

On the Borel summability of formal solutions of certain higher-order linear ordinary differential equations

We consider a class of nth-order linear ordinary differential equations with a large parameter u. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of u. We demonstrate that, given mild conditions on the potential functions of the equation, the formal solutions are Borel summable with respect to the parameter u in large, unbounded domains of the independent variable. We establish that the formal series expansions serve as asymptotic expansions, uniform with respect to the independent variable, for the Borel re-summed exact solutions. Additionally, we show that the exact solutions can be expressed using factorial series in the parameter, and these expansions converge in half-planes, uniformly with respect to the independent variable. To illustrate our theory, we apply it to an nth-order Airy-type equation.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Jacobian-free Newton-Krylov method for multilevel nonlocal thermal equilibrium radiative transfer problems

Context. The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependence of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the nonlocal thermodynamical equilibrium (NLTE) problem. Aims. Our goal is to develop an efficient and rapidly converging method to solve the NLTE problem under the assumption of statistical equilibrium. In particular, we explore whether the Jacobian-Free Newton-Krylov (JFNK) method can be used. This method does not require an explicit construction of the Jacobian matrix because it estimates the new correction with the Krylov-subspace method. Methods. We implemented an NLTE radiative transfer code with overlapping bound-bound and bound-free transitions. This solved the statistical equilibrium equations using a JFNK method, assuming a depth-stratified plane-parallel atmosphere. As a reference, we also implemented the Rybicki & Hummer (1992) method based on linearization and operator splitting. Results. Our tests with the Fontenla, Avrett and Loeser C model atmosphere (FAL-C) and two different six-level Ca II and H I atoms show that the JFNK method can converge faster than our reference case by up to a factor 2. This number is evaluated in terms of the total number of evaluations of the formal solution of the radiative transfer equation for all frequencies and directions. This method can also reach a lower residual error compared to the reference case. Conclusions. The JFNK method we developed poses a new alternative to solving the NLTE problem. Because it is not based on operator splitting with a local approximate operator, it can improve the convergence of the NLTE problem in highly scattering cases. One major advantage of this method is that it is expected to allow for a direct implementation of more complex problems, such as overlapping transitions from different active atoms, charge conservation, or a more efficient treatment of partial redistribution, without having to explicitly linearize the equations.

On formal series solutions to 4th-order quadratic homogeneous differential equations and their convergence

Abstract It is known that all τ functions of the Painlevé equations satisfy the fourth-order quadratic differential equation. Among them, for the III, V, and VI equations, it is possible to express the formal series solutions combinatorially by using conformal blocks. In this paper, we show the convergence of the formal series, including the solutions of more general equations. The convergence of the conformal block function also follows in the case c = 1 by the absolute convergence of τ series, since it is a partial sum of the τ series. We also characterized the form of a homogeneous quadratic equation with a series solution similar to the tau functions of the Painlevé equations.

On Formal Solutions to $ q $-Difference Equations Containing Logarithms

On Formal Solutions to $ q $-Difference Equations Containing Logarithms

The Development of a Malleable Model for Critical System Supervision Integration

Critical systems, in which failure and malfunction may result in severe human, environmental, and financial damages, are essential components in various sectors and particularly in energy domains. Although undesirable, integration error problems in the supervision of critical systems do occur, incurring significant expenses due to an operator’s subjective analysis and hardware topology failures. In this work, a malleable model design approach is proposed to formulate and solve the integration error problem in critical systems’ supervision in terms of reliability. A real hybrid power plant (HPP) case is considered for a case study with simulated data. A method framework with an informal approach (C4 diagram) and formal approach (hierarchical colored Petri nets) in a radial spectrum is applied to the HPP supervision design. In using formal methods, a formulation and solution to this problem through structured, scalable, and compact mathematical representations are possible. This malleable model is intended to guarantee the functional correctness and also reliability of the plant supervision system based on system software architecture. The outcomes suggest that the malleable model is appropriate for the energy domain and can be used for other types of critical systems, bringing all the benefits of this methodology to the context in which it will be applied.