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For a measure $\mu$ on ${ℝ}^n$ with density that has a positive degree of homogeneous and a positive degree of concavity, we study the Orlicz–Minkowski problem for such general measure $\mu$ and show the existence of the even Orlicz–Minkowski problem for $\mu$. We also introduce the general Orlicz geominimal $\mu$-measures and show the existence of the Orlicz-Petty bodies for the general measure $\mu$, and hence prove the continuity of the general Orlicz geominimal $\mu$-measure.

Petty proved that a convex body in ${ℝ}^n$ has the minimal surface area among its $\mathrm{\text{SL}}(n)$ images if and only if its surface area measure is isotropic. In this paper, we seek the general minimal Orlicz surface area of a convex body containing the origin in its interior among its $\mathrm{\text{SL}}(n)$ images for a measure $\mu$ on ${ℝ}^n$ with density that has a positive degree of homogeneous, demonstrate the existence of the extreme body, and establish a necessary condition for the extreme body. Moreover, we also provide a counterexample to negate the uniqueness of the extreme body attaining the general minimal Orlicz surface area for $\mu$.

We introduce a family of multiplicative distributions {μ_s|s∈(0,1)} on a free group F and study it as a whole. In this approach, the measure of a given set R⊆F is a function μ(R) : s → μ_s(R), rather then just a number. This allows one to evaluate sizes of sets using analytical properties of their measure functions μ(R). We suggest a new hierarchy of subsets R in F with respect to their size, which is based on linear approximations of the function μ(R). This hierarchy is quite sensitive, for example, it allows one to differentiate between sets with the same asymptotic density. Estimates of sizes of various subsets of F are given.

Open innovation (OI) events are potent instruments for the development of dynamic ecosystems. However, the literature analyses the structure and mechanisms of OI events insufficiently to demonstrate their efficacy, making it difficult to justify the investments necessary for their success. With better data confirming their impact, funding for OI events should improve by becoming more accessible and, therefore, more conducive to efficient value creation. This regional study contributes to the literature on innovation ecosystems and field-configuring events by responding to the call for more effective measures of OI events to coordinate and improve the ecosystems’ overall competitiveness. Based on an analysis of six in-depth case studies, 28 semi-structured interviews, and secondary sources, we identify 54 best practices and 34 indicators of an event’s success for various actor types. Moreover, we suggest 11 measures of the short- and long-term impacts of an event on its ecosystem.

Small and medium-sized enterprises (SMEs) are considered the backbone of the Indian economy. But for the last few years, a large numbers of issues have been generating severe hurdles for the small and medium-sized enterprises in India. As SMEs enter the new era of globalisation and face different kinds of dramatic challenges, an attempt has been made to examine those challenges and determine the measures to overcome such types of challenges. For the present study, data have been gathered from entrepreneurs of the IT sector, banking sector and pharmaceutical sector. A sample of 240 entrepreneurs, i.e., eighty from each sector, was taken. The primary data were gathered with the help of a questionnaire on a five-point Likert scale and analysed by various descriptive statistics such as frequency distribution, mean and standard deviation. ANOVA and Factor analysis have been used to test research hypotheses and validate the results of the study. The analysis shows that entrepreneurs have to face various types of issues and challenges, and such challenges can be solved by reducing the compliances of the listing procedure, using social media for advertisements conducting business conferences and seminars periodically, providing tax incentives to the investors and minimising the risk factor.

Combined with cases of energy-saving existing building from home and abroad, this passage discusses about the reconstruction condition of existing buildings and makes a comparison by analyzing the existing buildings in terms of energy-saving technologies and relevant policies, which points out the existing energy-saving problems of existing buildings in Hot Summer and Warm Winter Zones in our country. Also, it sums up the experience of energy-saving reconstruction and finally proposes energy-saving measures.

According to rule No. 43 of Safety Regulations for Fireworks and Firecrackers, the illegal fireworks and firecrackers, which are confiscated or discarded by producers or sellers, should be sealed in situ and destructed by police. During the process of destruction, there may be unexpected combustion or explosion due to the inherent risk properties of fireworks and firecrackers, which leads to serious threats to the safety of people on the spot and even affects the safety and stability of the society. Consequently, it is of great importance to fully understand the risks of fireworks and firecrackers destruction, and eliminate the potential dangers in this process by taking effective fire safety measures from the aspects of people, objects and environment.