Time-space-direction Extension TRIZ Innovation Model for Product Innovation

In order to solve the problem that college students are prone to thinking set and direction deviation in the process of innovation practice. TRIZ (Latin abbreviation of "Teoriya Resheniya Izoblatelskikh Zadatch", which means theory of the solution of innovative problems) is extended and matched with the meta conditional features or quantities of the three dimensions of TSD (time, space and direction) of the problem. In this paper, TRIZ-TSD extension problem solving model is proposed to find compatible solutions. TRIZ-TSD extension problem solving model expands the available resources of the original TRIZ analysis tools, strengthens the interaction between the analysis tools, and makes it more suitable for beginners to use in practical innovation. Taking the university student innovation award-winning project "the intelligent wall planting system" as an example, the basic process and practical effect of TRIZ-TSD fusion innovation model in solving specific problems are verified. The basic principle and thinking mode of this method is not only limited to the practice of College Students’ innovation projects, but also has certain reference value for solving problems in other fields.

Hardy type inequalities for the fractional relativistic operator

<abstract><p>We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringer.</p></abstract>

The Role of Genetic Algorithm Selection Operators in Extending WSN Stability Period: A Comparative Study

A genetic algorithm (GA) contains a number of genetic operators that can be tweaked to improve the performance of specific implementations. Parent selection, crossover, and mutation are examples of these operators. One of the most important operations in GA is selection. The performance of GA in addressing the single-objective wireless sensor network stability period extension problem using various parent selection methods is evaluated and compared. In this paper, six GA selection operators are used: roulette wheel, linear rank, exponential rank, stochastic universal sampling, tournament, and truncation. According to the simulation results, the truncation selection operator is the most efficient operator in terms of extending the network stability period and improving reliability. The truncation operator outperforms other selection operators, most notably the well-known roulette wheel operator, by increasing the stability period by 25.8% and data throughput by 26.86%. Furthermore, the truncation selection operator outperforms other selection operators in terms of the network residual energy after each protocol round.

Optimal control for cooperative systems involving fractional Laplace operators

In this work, the elliptic $2\times 2$ 2 × 2 cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.

Level-Planar Drawings with Few Slopes

We introduce and study level-planar straight-line drawings with a fixed number $$\lambda $$ λ of slopes. For proper level graphs (all edges connect vertices of adjacent levels), we give an $$O(n \log ^2 n / \log \log n)$$ O ( n log 2 n / log log n ) -time algorithm that either finds such a drawing or determines that no such drawing exists. Moreover, we consider the partial drawing extension problem, where we seek to extend an immutable drawing of a subgraph to a drawing of the whole graph, and the simultaneous drawing problem, which asks about the existence of drawings of two graphs whose restrictions to their shared subgraph coincide. We present $$O(n^{4/3} \log n)$$ O ( n 4 / 3 log n ) -time and $$O(\lambda n^{10/3} \log n)$$ O ( λ n 10 / 3 log n ) -time algorithms for these respective problems on proper level-planar graphs. We complement these positive results by showing that testing whether non-proper level graphs admit level-planar drawings with $$\lambda $$ λ slopes is -hard even in restricted cases.

Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects.

The extension problem for fractional Sobolev spaces with a partial vanishing trace condition

We construct whole-space extensions of functions in a fractional Sobolev space of order $$s\in (0,1)$$ s ∈ ( 0 , 1 ) and integrability $$p\in (0,\infty )$$ p ∈ ( 0 , ∞ ) on an open set O which vanish in a suitable sense on a portion D of the boundary $${{\,\mathrm{\partial \!}\,}}O$$ ∂ O of O. The set O is supposed to satisfy the so-called interior thickness condition in$${{\,\mathrm{\partial \!}\,}}O {\setminus } D$$ ∂ O \ D , which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case $$D=\emptyset $$ D = ∅ using a geometric construction.

Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups

Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 4238–4294. They concern Propositions 3.12–3.13, and Theorem 1.5, Corollary 1.6 and Remark 4.10. The purpose of this corrigendum is to point out the errors and supply necessary modifications where it is applicable.