Size Formula Research Articles

Enhanced ICL Sizing Accuracy Using Advanced Optical Coherence Tomography-Based Predictive Formula

The aim of this study was to evaluate the accuracy of existing implantable collamer lens (ICL) sizing formulas, specifically the NK and KS formulas using CASIA2 and ANTERION devices, and to introduce a novel method aimed at improving the predictability of postoperative vault outcomes. Retrospective case series. Preoperative measurements were taken using both CASIA2 and ANTERION devices. The efficacy of the NK and KS formulas, which are integrated into CASIA2, was assessed by comparing their predicted vault values against actual postoperative measurements obtained one month after surgery. A stepwise multiple regression analysis was performed with the aim of developing a new, more accurate predictive formula for optimal ICL sizing. When compared to the existing NK and KS formulas, the new formula developed from ANTERION measurements demonstrated superior accuracy in predicting optimal ICL size, with a mean vault of 0.535 ± 0.200 mm, compared to 0.419 ± 0.172 mm and 0.466 ± 0.103 mm for the NK and KS formulas, respectively. The regression analysis identified several significant parameters influencing the determination of optimal ICL size. This study presents a novel formula for ICL sizing that leverages measurements from the ANTERION device, supported by a detailed multiple regression analysis. The findings suggest that this new approach significantly enhances the accuracy of ICL size prediction, potentially reducing the risk of complications associated with improper sizing.

Exact Integral Formulas for False Discovery Rate and the Variance of False Discovery Proportion.

Multiple hypothesis testing is an integral component of data analysis for large-scale technologies such as proteomics, transcriptomics, or metabolomics, for which the false discovery rate (FDR) and positive FDR (pFDR) have been accepted as error estimation and control measures. The pFDR is the expectation of false discovery proportion (FDP), which refers to the ratio of the number of null hypotheses to that of all rejected hypotheses. In practice, the expectation of ratio is approximated by the ratio of expectation; however, the conditions for transforming the former into the latter have not been investigated. This work derives exact integral expressions for the expectation (pFDR) and variance of FDP. The widely used approximation (ratio of expectations) is shown to be a particular case (in the limit of a large sample size) of the integral formula for pFDR. A recurrence formula is provided to compute the pFDR for a predefined number of null hypotheses. The variance of FDP was approximated for a practical application in peptide identification using forward and reversed protein sequences. The simulations demonstrate that the integral expression exhibits better accuracy than the approximate formula in the case of a small number of hypotheses. For large sample sizes, the pFDRs obtained by the integral expression and approximation do not differ substantially. Applications to proteomics data sets are included.

Recognition Strategy and Performance of Non-Teaching Staff at University of Eldoret in Kenya

Non-academic staff contribute significantly to the effective functioning of universities across the globe, supporting the institution's mission of education, research, and service to society. Their roles are diverse and essential, helping to create a supportive and conducive environment for academic excellence and student success. Their performance is aligned with broader national development priorities and the global agenda set forth by the SDGs. Their contributions are essential for advancing education, fostering innovation, promoting sustainable development, and building inclusive societies. By recognizing and supporting the role of non-academic staff, governments and institutions can better harness their potential to contribute to positive social, economic, and environmental outcomes. By facilitating access to quality education, they help build the knowledge and skills necessary for individuals to participate effectively in society and contribute to economic development. Unlike academic staff, whose work is more closely tied to research and teaching, the roles of non-academic staff, may not always be as directly connected to the core mission of the institution. This disconnect has led to several challenges that demotivate the work of non-teaching staffs. The purpose of this study was to examine the extent to which employee recognition strategy has influenced the performance of non-academic staff in the UOE, in Kenya. The study based on a quantitative research approach and underpinned by Maslow Theory of Motivation. The researcher used a correlational research design to establish the relationship between the study variables. The target population of this study comprised all the 208 permanent non-teaching staff in the university of Eldoret from which 137 were picked as sample size of the study Yamane formula. Stratified random sampling and simple random samplings were used to select respondents for the study. The study used structured self-administered questionnaires as its main primary data collection tool. Descriptive and inferential statistics were used to analyze data with the aid of the Statistical Package for Social Sciences (SPSS) version 25. Descriptive statistics included percentages, frequencies, mean and standard deviation. Inferentially, regression analysis was applied to get the changes in dependent variable caused by the influence of independent variables. Analyzed data was presented in form of tables, suitable graphs based on the APA format. The study results revealed that there was positive linear effect of influence of recognition on employee’s performance (β1=0.798, p=0.000 < 0.05). The study concluded that there is a significant relationship between recognition and performance of non-academic staff in the University of Eldoret.

Separators in Continuous Petri Nets

Leroux has proved that unreachability in Petri nets can be witnessed by a Presburger separator, i.e. if a marking $\vec{m}_\text{src}$ cannot reach a marking $\vec{m}_\text{tgt}$, then there is a formula $\varphi$ of Presburger arithmetic such that: $\varphi(\vec{m}_\text{src})$ holds; $\varphi$ is forward invariant, i.e., $\varphi(\vec{m})$ and $\vec{m} \rightarrow \vec{m}'$ imply $\varphi(\vec{m}'$); and $\neg \varphi(\vec{m}_\text{tgt})$ holds. While these separators could be used as explanations and as formal certificates of unreachability, this has not yet been the case due to their worst-case size, which is at least Ackermannian, and the complexity of checking that a formula is a separator, which is at least exponential (in the formula size). We show that, in continuous Petri nets, these two problems can be overcome. We introduce locally closed separators, and prove that: (a) unreachability can be witnessed by a locally closed separator computable in polynomial time; (b) checking whether a formula is a locally closed separator is in NC (so, simpler than unreachability, which is P-complete). We further consider the more general problem of (existential) set-to-set reachability, where two sets of markings are given as convex polytopes. We show that, while our approach does not extend directly, we can efficiently certify unreachability via an altered Petri net.

Optimization of Soursop (Annona muricata L.) Leaf Extract in Nanoemulgel and Antiacnes Activity Test Against Propionibacterium acnes, Staphylococcus aureus, Staphylococcus epidermidis Bacteria

Soursop leaf extract (Annona muricata L.) has antibacterial activity with active components of alkaloids, flavonoids, steroids, and saponins. This research aims to optimize the use of VCO, Tween 80, and PEG 400 in the nanoemulsion system, which will be added Carbopol 940 as a gelling agent to form a nanoemulgel and to determine antibacterial activity. By utilizing the simplex lattice design method in Design Expert 13.0, the nanoemulsion formula has been successfully optimized involving a mixture of VCO, Tween 80, and PEG 400. A total of 14 different nanoemulsion formulas were produced through this process. The process of making nanoemulsion is carried out by mixing extracts, oils, surfactants and cosurfactants, homogenized using a vortex, then sonicated. Evaluation of % transmittance, emulsification time, and pH were carried out to determine nanoemulsion physical properties. The nanoemulsion optimal formula was evaluated for particle size, polydispersity index, and zeta potential and made into nanoemulgel with the addition of Carbopol 940. The optimal formula has a composition of 10.86% VCO, 67.33% Tween 80, 21.81% PEG 400 form homogeneous and clear nanoemulsion with % transmittance of 91.97±1.11%, emulsification time of 56.42±0.72 seconds, and pH of 5.67±0.24. Particle size, polydispersity index, and zeta potential of the optimal formula were 229.47±38.79 nm, 0.41±0.10, and -39.13±0.19 mV, respectively. Evaluation of nanoemulgel physical properties showed homogeneous, pH value of 5.83±0.24, spreadability of 5.57±0.25 cm, adhesive force of 3.80±0.25 seconds, viscosity of 11479.33±167.49 cP, antibacterial activity against P. acnes, Staphylococcus aureus, and Staphylococcus epidermidis with inhibition zone diameters of 9.67±0.47 mm, 7.33±0.47 mm, and 5.67±0.47 mm. respectively. Nanoemulgel soursop leaf extract has suitable physical properties, and antibacterial activity is in the medium category.

Signal temporal logic synthesis under Model Predictive Control: A low complexity approach

In this paper, we focus on the challenging problem of model predictive control (MPC) for dynamics systems with high-level tasks formulated as signal temporal logic (STL). The state-of-art for STL synthesis mainly suffers from limited scalability with respect to the complexity of the task and the planning horizon, hindering the real-time implementation of MPC. This work tackles this issue by STL formula reformulation and input blocking. Specifically, simplifications are applied on disjunctive STL (sub)formulae recursively in the framework of MPC to limit formula size. We show that the simplified STL can be reformulated into mixed integer linear programming (MILP) constraints with a modifiable number of binary variables being required. The move blocking scheme is then employed to further reduce problem complexity by fixing input variables to be constant over several time intervals. In order to trade off the control performance and computational load, a blocking structure design with on-line correction is proposed. The extension of the proposed STL-MPC algorithm to uncertain systems is achieved through STL constraint tightening. Simulations and experiments show the effectiveness of the proposed algorithm.

Mapping singly-linked rules to linear temporal logic formulas

Business services are provided by enacting interrelated business processes. Service providers must ensure enactments comply with policies, regulations, and business rules, including rules with quantitative time constraints. Enforcing such rules at design-time may be too restrictive, so effective service provisioning includes expressing rules in a formal specification language and detecting violations of these rules at runtime. Many specification languages do not include quantitative time constraints; for languages with such constraints, it is often unknown if they have runtime monitors whose auxiliary data storage is of bounded size. In this paper, we formulate a technical model of services, a logic language with quantitative time constraints for specifying rules, and develop techniques for automatically generating monitors to detect rule violations. This approach involves two steps, translating: (1) rules to formulas in linear temporal logic (LTL) on finite traces, and (2) LTL formulas to finite state machines. Since algorithms exist for step (2), we focus on step (1), i.e., mapping rules to equivalent LTL formulas. We present and establish the correctness of two translation techniques for “singly-linked” rules. We also compare the size of formulas produced by these techniques with a method of translation derived from Kamp’s Theorem, showing an improvement from hyper-exponential to exponential size.

Poverty Reduction and Sustainable Development Goals in Rural Areas in Nigeria: A Study of Selected Local Government Areas in Enugu State, Nigeria

This study examined poverty reduction and SDGs in rural areas in Nigeria with reference to selected local government areas in Enugu State. The study adopted the descriptive survey research design and made use of both primary and secondary sources of data. The population of the study was 722,664 people of the three local government areas selected to represent Enugu State, while the sample size was 400 derived via Taro Yamani formula size determination. The cluster sampling technique was applied to select the sample from the population of the study, while the data collected were presented and analyzed using frequency percentage and chi-square (X2) analysis. The study revealed a number of factors contributing to increasing rate of poverty in the rural areas in Nigeria -corruption, debt burden, unemployment, overdependence on oil, lack of political will, ethno-religious conflicts among others. The study also revealed the challenges of implementing SDGs to reduce poverty in rural areas in Nigeria -endemic corruption, lack of effective policies, lack of accountability, insecurity, poor infrastructure among others. The study discovered the SDGs based rural poverty reduction strategic framework in place for rural areas in Nigeria to include job creation, adequate budgetary allocation, integrated rural development program, provision of basic needs, creation of awareness, adoption of the basic needs strategy, full integration of the rural poor, targeting among others. Finally, the study also revealed bottom-up approach, capacity acquisition, provision of infrastructure, inter-agency cooperation, objective targeting among others as measures to efficient implementation of SDGs in rural poverty reduction in Nigeria. Based on these findings, the researchers recommended that the Nigerian government should address the issues of poverty reduction programs via effective implementation of poverty reduction related program/policies among others.

Tree-Depth and the Formula Complexity of Subgraph Isomorphism

For a fixed “pattern” graph , the colored -subgraph isomorphism problem (denoted by ) asks, given an -vertex graph and a coloring , whether contains a properly colored copy of . The complexity of this problem is tied to parameterized versions of and , among other questions. An overarching goal is to understand the complexity of , under different computational models, in terms of natural invariants of the pattern graph . In this paper, we establish a close relationship between the formula complexity of and an invariant known as tree-depth (denoted by). is known to be solvable by monotone formulas of size . Our main result is an lower bound for formulas that are monotone or have sublogarithmic depth. This complements a lower bound of Li, Razborov, and Rossman [SIAM J. Comput., 46 (2017), pp. 936–971] relating tree-width and circuit size. As a corollary, it implies a stronger homomorphism preservation theorem for first-order logic on finite structures [B. Rossman, An improved homomorphism preservation theorem from lower bounds in circuit complexity, in 8th Innovations in Theoretical Computer Science Conference, LIPIcs. Leibniz Int. Proc. Inform. 67, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2017, 27]. The technical core of this result is an lower bound in the special case where is a complete binary tree of height , which we establish using the pathset framework introduced in B. Rossman [SIAM J. Comput., 47 (2018), pp. 1986–2028]. (The lower bound for general patterns follows via a recent excluded-minor characterization of tree-depth [W. Czerwiński, W. Nadara, and M. Pilipczuk, SIAM J. Discrete Math., 35 (2021), pp. 934–947; K. Kawarabayashi and B. Rossman, A polynomial excluded-minor approximation of treedepth, in Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms, 2018, pp. 234–246]. Additional results of this paper extend the pathset framework and improve upon both the best known upper and lower bounds on the average-case formula size of when is a path.

Conformance checking artefacts through weighted partial MaxSAT

Conformance checking techniques are based on the computation of artefacts which enable the reasoning about observed behaviour of processes and their models. A family of these related artefacts, alignments, multi- and anti-alignments are defined over a distance function between observed behaviour and model replay, both represented as words from a given alphabet. Encoding this distance function, commonly the Levenshtein distance, into MaxSAT enables us to take advantage of state-of-the-art MaxSAT solvers. In this paper we provide an improvement upon previous SAT encodings for the alignment artefact family. We achieve a reduction in the resulting formula size while also obtaining good performance results on the computation of the artefacts. Additionally, we provide its direct extension that allows to easily change the cost function for the alignment computation and show the implementation of two particular examples from the literature: prefix matching prioritization and synchronization maximization.

Karakterisasi Nanokapsul Ekstrak Daun Serunai (Chromolaena odorata L.) dengan Variasi Kitosan-Alginat Menggunakan Metode Emulsi-Difusi

Serunai (Chromolaena odorata L.) is a plant that has been widely used in medicine, one of which is as an antidiabetic. But treatment using plant extracts has drawbacks to the solubility of the active substance and its bioavailability in the body. Nanocapsules are one of the systems in particle technology that can solve this problem by utilizing a polymer that will encapsulate the active substance and release it slowly at the intended target. To achieve this, the manufacture of nanocapsules must meet several characteristic requirements such as particle size, potential zeta, absorption efficiency, and emulsion stability. This study was conducted to identify the nanocapsules characteristics of Serunai leaf extract (Chromolaena odorata L.) with chitosan-alginate variations and identify the influence of chitosan-alginate variations on the characteristics of nanocapsules. This study is a laboratory experimental study with a one-group posttest-only design. The manufacture of Serunai leaf extract nanocapsules using the emulsion-diffusion method, which is then characterized including particle size determination, potential zeta determination, absorption efficiency test (%EE), and emulsion stability test. The results obtained from the determination of the particle size of Formula I 196.4 nm, Formula II 264.2 nm, and Formula III 207.4 nm, potential zeta Formula I -36.1 mV, Formula II -40.1 mV, and Formula III -36.5 mV, the formula I %EE values 99.7%, Formula II 99.8%, and Formula III 99.7%, as well as all formulas indicating the emulsion type m/a. Three formulas have met the requirements of nanocapsules characteristics. The formula is best obtained in Formula II with a chitosan concentration of 0.3% and alginate of 0.6%, so chitosan-alginate variations influence the characteristic results.

Quasilinear-time Computation of Generic Modal Witnesses for Behavioural Inequivalence

We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the paradigm of universal coalgebra. For every behavioural equivalence class in a given system, we construct a formula which holds precisely at the states in that class. The algorithm instantiates to deterministic finite automata, transition systems, labelled Markov chains, and systems of many other types. The ambient logic is a modal logic featuring modalities that are generically extracted from the functor; these modalities can be systematically translated into custom sets of modalities in a postprocessing step. The new algorithm builds on an existing coalgebraic partition refinement algorithm. It runs in time O((m+n) log n) on systems with n states and m transitions, and the same asymptotic bound applies to the dag size of the formulae it constructs. This improves the bounds on run time and formula size compared to previous algorithms even for previously known specific instances, viz. transition systems and Markov chains; in particular, the best previous bound for transition systems was O(mn).

FORMULASI DAN EVALUASI NANO HIDROGEL EKSTRAK DAUN SERUNAI (Chromolaena odorata L.) DENGAN VARIASI KONSENTRASI POLIMER CARBOPOL 980

Hydrogel is an ideal preparation as a wound dressing because it can provide a cold sensation that can reduce swelling in the wound area. Nanoparticles are particles that have a size of 1-1000 nm. Nanoparticles have the advantage of reducing the particle size and delivering the active substance to the target site. In the manufacture of nanohydrogels it is necessary to have a gelling agent in order to obtain a preparation that meets the requirements. In this study, nanohydrogels were made using Chrysanthemum leaf extract (Chromolaena odorata L.) as the active substance and made with various concentrations of carbopol 980 as a gelling agent. The purpose of this study was to determine the effect of variations in the concentration of carbopol 980 on nanohydrogel preparations of chrysanthemum leaf extract. The method used is Quasi Experimental Design. Simplicia was made into extracts and then made into nano preparations and evaluated. Data were analyzed using One Way Anova and Kruskal-Wallis. The particle size of Formula I nanohydrogel preparation was obtained at 412.9 nm. The results of the evaluation of the preparation showed that the nanohydrogel of chrysanthemum leaf extract with variations in the concentration of carbopol 980 had no effect on homogeneity, but it did affect the pH, viscosity, dispersibility, and adhesion test as shown in the One Way Anova statistical test (p<0.05). From the evaluation results, the ideal formula for nano hydrogel preparations was found in formula I with a carbopol 980 concentration of 0.5%.

Tacrolimus loaded lipid-polymer hybrid nanoparticles incorporated thermosensitive gel as intravesical drug delivery system

A drug that is administered through a catheter into the bladder is referred to as an intravesical drug delivery system. The aim of this work is to improvise intravesical drug delivery of Tacrolimus loaded lipid polymer hybrid nanoparticles thermosensitive gel for bladder wall to provide control release, increase intravesical residence time and avoid fast removal by urination. The Tacrolimus loaded lipid polymer hybrid nanoparticles mimic cell membrane and enhance cellular uptakes. Our data reveals nanocarrier formation with a mean particle size, zeta potential and entrapment efficiency of optimal formula was found to be 124±0.01 nm,-27.5±0.102mv and 72% ± 0.15% respectively. In situ gelling formulations containing TAC-CS-LPHNs can adhere to the mucosal layer of the bladder and help in the diffusion of therapeutic agent across the bladder wall. To impart mechanical strength and mucoadhesive properties, the chitosan concentration was adjusted to 0.5% and 0.25%.The image of field emission scanning electron microscope shows an irregular surface with filled pores with nanoparticles. The gel was syringeable and had reasonable viscosity within room temperature. A Tissue uptake study reveals that Tacrolimus loaded lipid polymer hybrid nanoparticles have been penetrating bladder tissues and accumulated inside the cytoplasm and nucleus of urothelium epithelial cells. In addition, the bioimaging study shows that the gel resided inside the bladder for up to 2 hrs and completely urinated out of the bladder with negligible distribution to other tissues.

Discovering the Roots: Uniform Closure Results for Algebraic Classes Under Factoring

Newton iteration is an almost 350-year-old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all roots simultaneously. In this form, the process yields better circuit complexity in the case when the number of rootsris small but the multiplicities are exponentially large. Our method sets up a linear system inrunknowns and iteratively builds the roots as formal power series. For an algebraic circuit\( f(x_1,\ldots ,x_n) \)of sizes, we prove that each factor has size at most a polynomial insand the degree of the squarefree part off. Consequently, if\( f_1 \)is a\( 2^{\Omega (n)} \)-hard polynomial, then any nonzero multiple\( \prod _{i} f_i^{e_i} \)is equally hard for arbitrary positive\( e_i \)’s, assuming that\( \sum _i\deg (f_i) \)is at most\( 2^{O(n)} \).It is an old open question whether the class of poly(n) size formulas (respectively, algebraic branching programs) is closed under factoring. We show that given a polynomialfof degree\( n^{O(1)} \)and formula (respectively, algebraic branching program) size\( n^{O(\log n)} \), we can find a similar-size formula (respectively, algebraic branching program) factor in randomized poly(\( n^{\log n} \)) time. Consequently, if the determinant requires an\( n^{\Omega (\log n)} \)size formula, then the same can be said about any of its nonzero multiples.In all of our proofs, we exploit the following property of multivariate polynomial factorization. Under a random linear transformation\( \tau \), the polynomial\( f(\tau \overline{x}) \)completely factors via power series roots. Moreover, the factorization adapts well to circuit complexity analysis. Therefore, with the help of the strong mathematical characterizations and the ‘allRootsNI’ technique, we make significant progress towards the old open problems; supplementing the vast body of classical results and concepts in algebraic circuit factorization (e.g., [17,51,54,111]).

New precise model of studentized principal components

If the sample Mahalanobis distance (SMD) is atypically large, it is essential to statistically estimate or test the contribution of each studentized principal component (SPC) decomposed from the SMD to consider its cause. However, there are no appropriate probability models for the SPCs of small samples. This study proposes a precise probability model for the SPCs of small samples without estimating the population eigenvalues or eigenvectors. The proposed model for an SPC comprises an elementary formula of sample size and the SPC’s index multiplied by one random variable following the t-distribution, which is simpler and requires no further computing compared with previous models. Numerical experiments demonstrated that the proposed model performs well under the weak condition that population eigenvalues are closely distinct with various dimensions and sample size. For practical implementation, the proposed model was applied for correcting the SMD to the population Mahalanobis distance, demonstrating better performance than other models. Additionally, the proposed model enables precise statistical testing of SPCs for discriminant analysis, cluster analysis, and projection pursuit, and the model improves the expectation–maximization algorithm for Gaussian mixture models.

Investigation on fatigue life prediction and reliability design of 304 stainless steel manufactured by laser metal deposition

Laser metal deposition (LMD) is an advanced technology to manufacture the specimen by layer-by-layer method. In this paper, the fatigue tests of 304 stainless steel (SS304) smooth specimens manufactured by LMD are conducted with the stress ratio of −1 and the frequency of 10 Hz. Considering that the fatigue crack is caused by the material defect on the subsurface, the fatigue life of smooth specimen under the different cyclic stress amplitudes are predicted based on the dislocation model, equivalent initial crack size and empirical formula. Lognormal, two-parameter Weibull and extreme maximum value distributions are applied to describe the fatigue life of the smooth specimens at the different cyclic stress amplitudes. The result shows that two-parameter Weibull distribution has the best ability to describe the fatigue life distribution. Based on two-parameter Weibull distribution, the probabilistic-stress-number ( P- S-N) curves at the four different reliability levels are plotted. Combined with the material strength degradation rule, the design checkpoint method is adopted to analyze the fatigue life reliability of smooth specimens under the different cyclic stress amplitudes. The reliability results are close to those of two-parameter Weibull distribution.

Analysis and optimization of few-mode fibers with low differential mode group delay by variational method

Mode-division multiplexing (MDM) technology based on few-mode fibers (FMFs) is the current research hotspot of optical fiber communication system because of its ability to increase the transmission capacity several times. When the number of multiplexed modes is large, the crosstalk between modes can be removed by multiple input multiple output digital signal processing algorithm at the receiving end. The larger the differential mode group delay (DMGD, <inline-formula><tex-math id="Z-20220504070336-1">\begin{document}$ \tau_{\rm DMGD} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070336-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070336-1.png"/></alternatives></inline-formula>), the more complex the algorithm is. Therefore, in order to reduce the complexity of the receiver, it is necessary to use FMFs with low DMGD. The variational method is proposed to analyze any FMFs with higher refractive index of core than that of cladding. The analytical formula of the fundamental mode size, the normalized propagation constant for each of all guided modes, and DMGD relative to the fundamental mode are derived. Moreover, their relationship with the normalized frequency and other fiber manufacturing parameters are given. On this basis, the graded-index FMFs are studied, and the fiber parameters are optimized. The optimization parameters are the difference between the maximum core refractive index and cladding refractive index <i>n</i><sub>1</sub> – <i>n</i><sub>2</sub> = 0.01, the core radius <i>a </i>= 14 μm, and the paramenter of refractive index distribution <i>α </i>= 1.975. In the optimized FMF, 6 LP modes can be guided and |<inline-formula><tex-math id="Z-20220504070445-1">\begin{document}$ \tau_{\rm DMGD} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070445-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20212198_Z-20220504070445-1.png"/></alternatives></inline-formula>| is less than 15 ps/km within the C band and L band. In the end, the effects of the fiber manufacturing errors on DMGD are discussed.

Development, Characterization and Evaluation of Ritonavir Nanosuspension Treatment of Antiretroviral Therapy

Oral nanosuspension of ritonavir was prepared by antisolvent precipitation method using various polymers such as Eudragit RS100, Poloxamer 407, SLS and Methanol.The effect of eudragit RS100 and poloxamer 407 used stabilizer and SLS is surfactant was investigated on particle size and distribution, drug content, entrapment efficiency was observed. Ritonavir is having low solubility and low permeability drug belonging to class-IV according to BCS. Drug-excipient compatibility and amorphous nature of ritonavir drug is prepared nanosuspension was confirmed by FTIR, DSC and Motic microscope studies, respectively. The nanosuspension was further evaluated for drug content, saturation solubility study and entrapment efficiency. The average particle size of ritonavir nanaosuspensions formulas was observed from 0.006 µm to 0.017 µm. The studied in the solubility and dissolution rate there are the increase solubility and dissolution rate of ritonavir nanosuspension.

On the Satisfiability and Model Checking for one Parameterized Extension of Linear-time Temporal Logic

Sequential reactive systems are computer programs or hardware devices which process the flows of input data or control signals and output the streams of instructions or responses. When designing such systems one needs formal specification languages capable of expressing the relationships between the input and output flows. Previously, we introduced a family of such specification languages based on temporal logics $LTL$, $CTL$ and $CTL^*$ combined with regular languages. A characteristic feature of these new extensions of conventional temporal logics is that temporal operators and basic predicates are parameterized by regular languages. In our early papers, we estimated the expressive power of the new temporal logic $Reg$-$LTL$ and introduced a model checking algorithm for $Reg$-$LTL$, $Reg$-$CTL$, and $Reg$-$CTL^*$. The main issue which still remains unclear is the complexity of decision problems for these logics. In the paper, we give a complete solution to satisfiability checking and model checking problems for $Reg$-$LTL$ and prove that both problems are Pspace-complete. The computational hardness of the problems under consideration is easily proved by reducing to them the intersection emptyness problem for the families of regular languages. The main result of the paper is an algorithm for reducing the satisfiability of checking $Reg$-$LTL$ formulas to the emptiness problem for Buchi automata of relatively small size and a description of a technique that allows one to check the emptiness of the obtained automata within space polynomial of the size of input formulas.