The interplay of different metrics for the construction of constant dimension codes

<p style='text-indent:20px;'>A basic problem for constant dimension codes is to determine the maximum possible size <inline-formula><tex-math id="M1">\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> of a set of <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-dimensional subspaces in <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_q^n $\end{document}</tex-math></inline-formula>, called codewords, such that the subspace distance satisfies <inline-formula><tex-math id="M4">\begin{document}$ d_S(U,W): = 2k-2\dim(U\cap W)\ge d $\end{document}</tex-math></inline-formula> for all pairs of different codewords <inline-formula><tex-math id="M5">\begin{document}$ U $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ W $\end{document}</tex-math></inline-formula>. Constant dimension codes have applications in e.g. random linear network coding, cryptography, and distributed storage. Bounds for <inline-formula><tex-math id="M7">\begin{document}$ A_q(n,d;k) $\end{document}</tex-math></inline-formula> are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show the potential for further improvements. As examples we give improved constructions for the cases <inline-formula><tex-math id="M8">\begin{document}$ A_q(10,4;5) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ A_q(11,4;4) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ A_q(12,6;6) $\end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id="M11">\begin{document}$ A_q(15,4;4) $\end{document}</tex-math></inline-formula>. We also derive general upper bounds for subcodes arising in those constructions.</p>

Solving a Triangle in Teaching Primary School Mathematics

The paper studies solving a triangle in primary school mathematics education. It proposes a system of problems reflecting the classification of the concept of triangle according to the sides and the angles. Each subsystem of a given main system includes a basic problem with generalized formulation and a sample solution followed by problems illustrating the basic problem. The methodological analysis encompasses some didactic components – short description, construction/drawing, sample solution, necessary component concepts, component pieces of knowledge and component problems. All drawings in the study have been made by using the mathematical software GeoGebra in order to ensure dynamism and clarity, and subsequently to achieve easier understanding of a problem and finding out its solution.

Case Article—Louisiana Branch Lines

Louisiana Branch Lines is a struggling Southeast U.S. railroad in just four cities and 12 markets. Their marketing, operations, and finance performance is poor and their departments disjointed. In this customizable, nine-part case, instructors can choose to focus on basic problem structuring and descriptive and predictive statistics, optimization model building, simulation of solutions, or the integration of all of the above. It is based on a real-world case.

Collaborative calculation and application of interreal and real interval relations to protect privacy

The determination of the relation between a number and a numerical interval is one of the core problems in the scientific calculation of privacy protection. The calculation of the relationship between two numbers and a numerical interval to protect privacy is also the basic problem of collaborative computing. It is widely used in data queries, location search and other fields. At present, most of the solutions are still fundamentally limited to the integer level, and there are few solutions at the real number level. To solve these problems, this paper first uses Bernoulli inequality generalization and a monotonic function property to extend the solution to the real number level and designs two new protocols based on the homomorphic encryption scheme, which can not only protect the data privacy of both parties involved in the calculation, but also extend the number domain to real numbers. In addition, this paper designs a solution to the confidential cooperative determination problem between real numbers by using the sign function and homomorphism multiplication. Theoretical analysis shows that the proposed solution is safe and efficient. Finally, some extension applications based on this protocol are given.

An Analysis of Zeno’s Paradox and Non-measurable Sets Based on Dialectical Infinity

The Problem of Continuity and Discreteness is the basic problem of philosophy and mathematics. For a long time, there is no clear understanding of this problem, which leads to the stagnation of the problem, because the essence of the problem is a problem of finity and infinity. The essence of the philosophical thought on which the mathematical definition of “line segment is composed of dots” is the idea of actual infinity, and geometric dot is equivalent to algebraic zero in terms of measure properties. In view of the above contradictions, this paper presents two solutions satisfying both the philosophical and mathematical circles based on the view of dialectical infinity, and the authors make a deep analysis of Zeno’s paradox and the non-measurable set based on both solutions.

Aplikasi Kasir Pada Adibah Boutique Berbasis Desktop

Computers as human aids have advantages including speed, accuracy, and efficiency in data processing compared to manual systems. Computers have spread in various fields, both in the world of education and the world of work, including in the field of sales. Adibah Boutique has problems in terms of, among others, the irregularity of the management system, especially profit and loss, sales calculations (transaction activities), data collection of goods and preparation of sales reports still using manuals, cashier operators still use worksheet applications to complete each work activity, thus providing the impression of an impact that is less effective and efficient in terms of time and energy generated every day. Another problem in terms of the goods coding system and the absence of evidence between the seller and the buyer after the transaction raises a very basic problem, one solution is to use a desktop-based application that can manage sales information systems more easily thereby reducing the problems that occur in The Adibah Boutique. This application can be used as a commercial medium by the owner or staff of Adibah Boutique to make it easier to make sales transactions to consumers.

Using numerical methods to design simulations: revisiting the balancing intercept

We consider methods for generating draws of a binary random variable whose expectation conditional on covariates follows a logistic regression model with known covariate coefficients. We examine approximations for finding a “balancing intercept,” that is, a value for the intercept of the logistic model that leads to a desired marginal expectation for the binary random variable. We show that a recently proposed analytical approximation can produce inaccurate results, especially when targeting more extreme marginal expectations or when the linear predictor of the regression model has high variance. We describe and implement a numerical approximation based on Monte Carlo methods that appears to work well in practice. Our approach to the basic problem of the balancing intercept provides an example of a broadly applicable strategy for formulating and solving problems that arise in the design of simulation studies used to evaluate or teach epidemiologic methods.

Integration of Migrants in a Major Polish City. Kraków’s Public Cultural Institutions and the “New Ukrainians”

The article deals with the integration processes of Polish native inhabitants of Kraków and the newest (since 2014) migrants from Ukraine (70–100,000 in a city of about 800,000). One of the main actors in these processes are municipal public cultural institutions. Using a number of methods, the needs of the Ukrainian population in Kraków were assessed and the offer of the local public institutions was studied. A focus group, IDIs, analysis of websites, Facebook profiles, and participatory observation were used. A basic problem for migrants is finding information on the local cultural offer presented in Ukrainian or Russian. Kraków does much to include foreigners into its social life. However, still closer integration, taking advantage of the potential of migrants, would be instrumental to making their life better and to making the city even more attractive to its Polish and non-Polish inhabitants and tourists. Premises and other resources at the disposal of Ukrainian private institutions are too small for large-scale cultural activity. Kraków’s cafes and pubs help, organizing concerts and meet-the-author and meet-the-artist sessions, but these events could be better organized by public cultural institutions, inviting much larger audiences. Sometimes leading Ukrainian artists visit Kraków and turn to municipal institutions looking for support and employment, only to find neither. It would be very beneficial for the city to monitor these initiatives, via Kraków’s Ukrainian websites and Facebook profiles, and take advantage of them.

MATERNAL LEUKOCYTOSIS AS DIAGNOSTIC MARKERS IN SPONTANEOUSLY DECLARED PRETERM BIRTH

Spontaneous preterm birth is the basic problem of perinatal mortality in Bulgaria. Pregnancy is characterized by physiological leukocytosis - determined by twice increased neutrophils levels, unchanged monocyte levels, and a reduction in the levels of lymphocytes, eosinophils, and basophils. The leukocytosis is particularly pronounced in the last trimester, due to physiological stress during pregnancy, and it is a result of the increased inflammatory response, a consequence of selective immune tolerance, immunosuppression, and fetus-immunomodulation. The objective of this study was to investigate and to appreciate maternal leukocytosis as potential diagnostic markers in spontaneously declared preterm birth and term birth declared cases. Methods: The case–control study was performed in UMBAL-City Hospital, Stara Zagora during 2017–2020. The study involved 200 patients, split into two groups: G1- the healthy pregnant women, n1=100 with а registered singleton pregnancy, at gestational age 37-39+6, gave birth on the term (TB); G2- the PTB patients, n2=100, confirmed clinically by cardiotocography for gestation >32 weeks. The highly sensitive Leuko-TIC-ELISA-WBC (upper limit of the normal number of Leuc during pregnancy - 15x109 per L) test was used for investigation. Blood samples were taken by puncture of the v.cubitalis in an anticoagulant at the time of hospitalization and examined within 1 hrs. Patients with systemic chronic illness and infections were excluded from the study. The results showed statistically significant Leuc reduction in SPTB patients (14.31±2.66×109/L, p>0.03), compared to the increased (14.67±3.21×109/L) (in normal-15x109L) Leuc values in the TB group.In conclusion, the results of the Leuc value confirm the presence of a systemic leukocytosis/oxidative inflammatory reaction at the time of declaring SPTB and TB.

A characterization of Riesz-dual sequences which are near-Markushevich bases

The concept of Riesz-duals of a frame is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet analysis. In this paper, we introduce various alternative Riesz-duals, with a focus on what we call Riesz-duals of type I and II. Next, we provide some characterizations of Riesz-dual sequences in Banach spaces. A basic problem of interest in connection with the study of Riesz-duals in Banach spaces is that of characterizing those Riesz-duals which can essentially be regarded as M-basis. We give some conditions under which an Riesz-dual sequence to be an M-basis for [Formula: see text].