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We investigate Hopf braces, a concept recently introduced by Angiono, Galindo and Vendramin [I. Angiono, C. Galindo and L. Vendramin, Hopf braces and Yang–Baxter operators, Proc. Amer. Math. Soc.145 (2017) 1981–1995] in connection to the quantum Yang–Baxter equation. More precisely, we propose two methods for constructing Hopf braces. The first one uses matched pairs of Hopf algebras while the second one relies on category-theoretic tools.

We study relation varieties, i.e. classes of relational sets (resets) of the same type that are closed under the formation of products and retracts. The notions of an irreducible reset and a representation of a reset are defined similarly to the ones for partially ordered sets. We give a characterization of finite irreducible resets. We show that every finite reset has a representation by minimal resets which are certain distinguished irreducible retracts. It turns out that a representation by minimal resets is a smallest one in some sense among all representations of a reset. We prove that non-isomorphic finite irreducible resets generate different relation varieties. We characterize categorical equivalence of algebras via product and retract of certain resets associated with the algebras. In the finite case the characterization involves minimal resets. Examples are given to demonstrate how the general theorems work for particular algebras and resets.

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Let $p\in (\frac{n}{n+1},1]$ and $f\in h^p({ℝ}^n)$ be the local Hardy space in the sense of D. Goldberg. In this paper, the authors establish two bilinear decompositions of the product spaces of $h^p({ℝ}^n)$ and their dual spaces. More precisely, the authors prove that $h^1({ℝ}^n)\times \mathrm{\text{bmo}}({ℝ}^n)=L^1({ℝ}^n)+h_{\ast }^{\mathrm{\Phi }}({ℝ}^n)$ and, for any $p\in (\frac{n}{n+1},1)$, $h^p({ℝ}^n)\times {\mathrm{\Lambda }}_{\alpha }({ℝ}^n)=L^1({ℝ}^n)+h^p({ℝ}^n)$, where $\mathrm{\text{bmo}}({ℝ}^n)$ denotes the local BMO space, ${\mathrm{\Lambda }}_{\alpha }({ℝ}^n)$, for any $p\in (\frac{n}{n+1},1)$ and $\alpha :=n(\frac{1}{p}-1)$, the inhomogeneous Lipschitz space and $h_{\ast }^{\mathrm{\Phi }}({ℝ}^n)$ a variant of the local Orlicz–Hardy space related to the Orlicz function $\mathrm{\Phi }(t):=\frac{t}{\mathrm{\text{log}}(e+t)}$ for any $t\in [0,\infty )$ which was introduced by Bonami and Feuto. As an application, the authors establish a div-curl lemma at the endpoint case.

Let $G$ be a finite group, $p$ a prime, $P$ a Sylow $p$-subgroup of $G$ and $d$ a power of $p$ such that $1<d<\left|P\right|$. Let $G_p^{\ast }$ denote the unique smallest normal subgroup of $G$ for which the corresponding factor group is abelian of exponent dividing $p-1$. Let ${𝔉}_1$, ${𝔉}_2$, ${𝔉}_3$ be classes of all $p$-groups, $p$-nilpotent groups and $p$-supersolvable groups, respectively, $G^{𝔉}$ be the $𝔉$-residual of $G$. Let $X\in \{{(G_p^{\ast })}^{{𝔉}_1},G^{{𝔉}_2},G^{{𝔉}_3}\}$. A subgroup $H$ of a finite group $G$ is said to have $\mathrm{\Pi }$-property in $G$, if for any $G$-chief factor $L/K$, $|G/K:N_{G/K}((H\cap L)K/K)|$ is a $\pi ((H\cap L)K/K)$-number. A normal subgroup $E$ of $G$ is said to be $p$-hypercyclically embedded in $G$ if every $p$-$G$-chief factor of $E$ is cyclic, where $p$ is a fixed prime. In this paper, we prove that $E$ is $p$-hypercyclically embedded in $G$ if and only if for some $p$-subgroups $H$ of $E$, $H\cap X$ have $\mathrm{\Pi }$-property in $G$.

In this paper, we consider the cancellation problem for direct products in the category of quantales. It is easy to see that quantales are not always cancelable. We show that indecomposable quantales, simple quantales, quantales without zero-divisors and quantales without nontrivial idempotent elements except the top element are cancelable. We also prove that each quantale can be embedded into a (unital) cancelable quantale.

This paper contributes to the understanding of the context dependency of open innovation. It does so by empirically analysing the relationship between innovation activities, firm characteristics and the degree of innovation openness of manufacturing companies in three European countries with varying degrees of technological development. Logistic regression analysis is used to study CIS data from Germany, Portugal and Bulgaria. In line with the contingency approach to open innovation, the results suggest that the appropriate open innovation strategy is context dependent, with similar practices and firm characteristics obtaining opposite relationship signs in different countries. Hence, it is important to take country idiosyncrasies into account when designing policies to promote open innovation.

Radical innovations start as product innovations in sub-systems of the socio-technical system. External triggers cause product innovations which in turn influence transitions of a socio-technical system. Socio-technical systems require configurations and/or customisations to multiple sub-systems not necessarily to ICT alone. Expansions to product innovations in the sub-systems are required to provide meaningful designs. Actors combine meaningful designs of various sub-systems and devise solutions and its adoption. Product innovations cumulate as stable designs when solutions meet end-users wants and needs, and require changes to policies, procedures, and methods used during devising and adoption of the solution. In other words, we require process innovations. The author using a single case study examines the above phenomena. The methods and theories towards process innovations assist in expanding the existing socio-technical transition theories, especially Multi-Level Perspective (MLP), thereby assisting actors in analysing, learning, adjusting, and internalise innovations while they navigate, struggle, and negotiate alternatives.

This study investigates whether organisational innovation has positive impacts on small and medium enterprises, using three waves of the South Korean innovation survey. While correcting for endogeneity, we find that the probability of achieving a process or product innovation conditional on organisational innovation increases in a linear fashion from small to large firms. Moreover, the effects of organisational innovation are more pronounced for process innovation relative to product innovation. We show that R&D performers who implement an organisational innovation have a greater probability of introducing a new product or process. We also show that larger R&D performing firms benefit more from organisational innovation than smaller firms. Finally, we find evidence that high-tech industries benefit more from organisational innovation, in accordance with one of our hypotheses.

We first introduced the notions of (anti-)fuzzy subhyperlattices. Then we proved that the (anti-)product of two (anti-)fuzzy subhyperlattices is a (anti-)fuzzy subhyperlattice. Lastly, we generalized some of our results to interval-valued fuzzy version.

Within a constantly competitive scenario, productive organizations have been looking for alternatives to improve all their internal processes in order to try to stay alive among competitors, in terms of economic, environmental and social sustainability. Thus, it is no longer common for someone or some isolated sector of a company to make a decision on their own. The decisions became collegiate. However, some sectors end up having more relevant arguments at each stage of a product’s great journey. At every moment of the process, from conceptualization (cradle) to disposal (grave or reuse), some departments become protagonists, while others become supporting actors. In this approach, the great journey of a product could be divided into “triangle of forces” structured by stakeholder representatives. The objective of this specific paper is to evaluate the activities of the conceptualization phase of a product that is observed as the first of these triangles whose vertices are formed by representatives from the Marketing, Industrial Design and Product Engineering areas. The proposed triangle model aims to organize the decision-making process during the development of a new product. Assigning leadership responsibilities and support functions to each sector at each stage of the project. This proposal would transform the great product journey into a star formed by these triangles of power, creating an agile and interactive environment of simultaneous engineering. As a result, this study presents a proposal of fundamental activities involved in the initial triangle of the task force conceptualization phase and the interrelationships among the areas of Marketing, Industrial Design and Product Engineering that happen along these processes.

Many large networks can be constructed from some existing small networks by using, in terms of graph theory, Cartesian product and Lexicographic product. The model of these networks possessing the property of small average distance and high connectivity which is a good network model. In this paper, we give the average distance and Wiener index of the Cartesian product of networks.

The pyrolysis characteristics of Chlorella vulgaris (C. Vulgaris) (one kind of microalgae) by microwave oven are studied. The microwave pyrolysis of C. Vulgaris is carried out under different dosages of C. Vulgaris and different contents of activated carbon. The products and pyrolysis temperature are analyzed in order to obtain the optimal conditions. The results indicate that with increasing the dosage of C. Vulgaris, pyrolysis temperature drops and pyrolysis time increases, the average heating rate has the decreasing tendency. The maximum bio-oil yield and gas yield are achieved under 30g of C. Vulgaris and 25g of C. Vulgaris, respectively. The optimal content of activated carbon is 5% with the maximum gas yield of 60.25% and the largest weight loss of 87.47%.