Given a $\sigma $-finite measure space $(X,\mu )$, a Young function $\Phi $, and a one-parameter family of Young functions $\{\Psi _q\}$, we find necessary and sufficient conditions for the associated Orlicz norms of any function $f\in L^\Phi (X,\mu )$ to satisfy

$$\begin{align*}\lim_{q\rightarrow \infty}\|f\|_{L^{\Psi_q}(X,\mu)}=C\|f\|_{L^\infty(X,\mu)}. \end{align*}$$

The constant C is independent of f and depends only on the family $\{\Psi _q\}$. Several examples of one-parameter families of Young functions satisfying our conditions are given, along with counterexamples when our conditions fail.

The functional analysis of technical systems is an important part of the design process. To further improve the design process, especially the functional analysis, it must not be viewed as a monodisciplinary process. To this end, cognitive factors such as the aha-experience must also be included in studies of analysis processes to a greater extent. This paper investigates the relationship between the occurrence of aha-experiences and the correctness of solutions in the analysis of a technical system. An aha-experience is a strong feeling of subjective certainty that accompanies the cognitive process of suddenly finding a previously unknown solution. For this purpose, a study on the functional analysis was evaluated. The results show that many identified subfunctions of the system under investigation were identified with an aha-experience and that these subfunctions are more often correct. The results also suggest that aha-experiences occur more often among students than among experienced design engineers. Especially among students, a positive relation of aha-experiences on the correctness of the identified subfunction can be seen. This offers potential for further investigations to make aha-experiences useful in design methods.

We compute the deficiency spaces of operators of the form $H_A{\hat {\otimes }} I + I{\hat {\otimes }} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor.47(38) (2014) 385301], but only proven under the restriction of $H_B$ having discrete, non-degenerate spectrum.

We prove uniform Hölder regularity estimates for a transport-diffusion equation with a fractional diffusion operator and a general advection field in of bounded mean oscillation, as long as the order of the diffusion dominates the transport term at small scales; our only requirement is the smallness of the negative part of the divergence in some critical Lebesgue space. In comparison to a celebrated result by Silvestre, our advection field does not need to be bounded. A similar result can be obtained in the supercritical case if the advection field is Hölder continuous. Our proof is inspired by Kiselev and Nazarov and is based on the dual evolution technique. The idea is to propagate an atom property (i.e., localisation and integrability in Lebesgue spaces) under the dual conservation law, when it is coupled with the fractional diffusion operator.

A key concern in beef production is how to improve carcass and meat quality traits. Identifying the genomic regions and biological pathways that contribute to explaining variability in these traits is of great importance for selection purposes. In this study, genome wide-association (GWAS) and pathway-based analyses of carcass traits (age at slaughter (AS), carcass weight (CW), carcass daily gain (CDG), conformation score and rib-eye muscle area) and meat quality traits (pH, Warner-Bratzler shear force, purge loss, cooking loss and colour parameters (lightness, redness, yellowness, chroma, hue)) were conducted using genotype data from the ‘GeneSeek Genomic Profiler Bovine LD’ array in a cohort of 1166 double-muscled Piemontese beef cattle. The genome wide-association analysis was based on the GRAMMAR-GC approach and identified 37 significant single nucleotide polymorphisms (SNPs), which were associated with 12 traits (P<5 × 10−5). In particular, 14 SNPs associated with CW, CDG and AS were located at 38.57 to 38.94 Mb on Bos taurus autosome 6 and mapped within four genes, that is, Leucine Aminopeptidase 3, Family with Sequence Similarity 184 Member B, Non-SMC Condensin I Complex Subunit G and Ligand-Dependent Nuclear Receptor Corepressor-Like. Strong pairwise linkage disequilibrium was found in this region. For meat quality traits, most associations were 1 SNP per trait, except for a signal on BTA25 (at ~11.96 Mb), which was significant for four of the five meat colour parameters assessed. Gene-set enrichment analyses yielded significant results for six traits (right-sided hypergeometric test, false discovery rate <0.05). In particular, several pathways related to transmembrane transport (i.e., oxygen, calcium, ion and cation) were overrepresented for meat colour parameters. The results obtained provide useful information for genomic selection for beef production and quality in the Piemontese breed.

Let $M$ be a $\text{II}_{1}$ factor and let ${\mathcal{F}}(M)$ denote the fundamental group of $M$. In this article, we study the following property of $M$: for any $\text{II}_{1}$ factor $B$, we have ${\mathcal{F}}(M\,\overline{\otimes }\,B)={\mathcal{F}}(M){\mathcal{F}}(B)$. We prove that for any subgroup $G\leqslant \mathbb{R}_{+}^{\ast }$ which is realized as a fundamental group of a $\text{II}_{1}$ factor, there exists a $\text{II}_{1}$ factor $M$ which satisfies this property and whose fundamental group is $G$. Using this, we deduce that if $G,H\leqslant \mathbb{R}_{+}^{\ast }$ are realized as fundamental groups of $\text{II}_{1}$ factors, then so are groups $G\cdot H$ and $G\cap H$.

In this article, we investigate the pointwise behaviors of functions on the Heisenberg group. We find wavelet characterizations for the global and local Hölder exponents. Then we prove some a priori upper bounds for the multifractal spectrum of all functions in a given Hölder, Sobolev, or Besov space. These upper bounds turn out to be optimal, since in all cases they are reached by typical functions in the corresponding functional spaces. We also explain how to adapt our proof to extend our results to Carnot groups.

Understanding product functions is a key aspect of the work undertaken by engineers involved in complex system design. The support offered to these engineers by existing modeling tools such as the function tree and the function structure is limited because they are not intuitive and do not scale well to deal with real-world engineering problems. A research collaboration between two universities and a major power system company in the aerospace domain has allowed the authors to further develop a method for function analysis known as function analysis diagram that was already in use by line engineers. The capability to generate and edit these diagrams was implemented in the Decision Rationale editor, a software tool for capturing design rationale. This article presents the intended benefits of the method and justifies them using an engineering case study. The results of the research have shown that the function analysis diagram method has a simple notation, permits the modeling of product functions together with structure, allows the generation of rich and accurate descriptions of product functionality, is useful to work with variant and adaptive design tasks, and can coexist with other functional modeling methods.

Our aim is to screen miRNAs and genes related to tetralogy of Fallot and construct a co-expression network based on integrating miRNA and gene microarrays. We downloaded the gene expression profile GSE35490 (miRNA) and GSE35776 (mRNA) of tetralogy of Fallot from the Gene Expression Omnibus database, which includes eight normal and 15 disease samples from infants, and screened differentially expressed miRNAs and genes between normal and disease samples (cut-off: p < 0.05; FDR < 0.05; and log FC > 2 or log FC < −2); in addition, we downloaded human miRNA and their targets, which were collected in the miRNA targets prediction database TargetScan, and selected ones that also appeared in our differentially expressed miRNAs and their predicted targets (score >0.9) and then made a relationship of diff_miRNAs and diff_genes of our results. Finally, we uploaded all the diff_target genes into String, constructed a co-expression network regulated by diff_miRNAs, and performed functional analysis with the software DAVID. Comparing normal and disease lesion tissue, we got 32 and 875 differentially expressed miRNAs and genes, respectively, and found hsa-miR-124 with 34 diff_target genes and hsa-miR-138 with two diff_target genes. Then we constructed a co-expression network that contains 231 pairs of genes. Genes in the network were enriched into 14 function clusters, and the most significant one is protein localisation. We screened the tetralogy of Fallot-related hsa-miR-124 and hsa-miR-138 with their direct and indirect differentially expressed target genes, and found that protein localisation is the significant cause affecting tetralogy of Fallot. Our approach may provide the groundwork for a new therapy approach to treating tetralogy of Fallot.