Snevily's Conjecture about L\mathcal{L}-intersecting Families on Set Systems and its Analogue on Vector Spaces

The classical Erd\H{o}s-Ko-Rado theorem on the size of an intersecting family of $k$-subsets of the set $[n] = \{1, 2, \dots, n\}$ is one of the fundamental intersection theorems for set systems. After the establishment of the EKR theorem, many intersection theorems on set systems have appeared in the literature, such as the well-known Frankl-Wilson theorem, Alon-Babai-Suzuki theorem, and Grolmusz-Sudakov theorem. In 1995, Snevily proposed the conjecture that the upper bound for the size of an $\mathcal{L}$-intersecting family of subsets of $[n]$ is ${{n} \choose {s}}$ under the condition $\max \{l_{i}\} < \min \{k_{j}\}$, where $\mathcal{L} = \{l_{1}, \dots, l_{s}\}$ with $0 \leq l_{1} < \cdots < l_{s}$ and $k_{j}$ are subset sizes in the family. In this paper, we prove that Snevily's conjecture holds for $n \geq {{k^{2}} \choose {l_{1}+1}}s + l_{1}$, where $k$ is the maximum subset size in the family. We then derive an analogous result for $\mathcal{L}$-intersecting families of subspaces of an $n$-dimensional vector space over a finite field $\mathbb{F}_{q}$.Comment: arXiv admin note: text overlap with arXiv:1701.00585 by other author

Numerical analysis of pressure fluctuation in a multiphase rotodynamic pump with air–water two-phase flow

International audiencePressure fluctuation in single-phase pumps has been studied widely, while less attention has been paid to research on multiphase pumps that are commonly used in the petroleum chemical industry. Therefore, this study investigates the pressure fluctuation for a multiphase rotodynamic pump handling air–water two-phase flow. Simulations based on the Euler two-fluid model were carried out using ANSYS_CFX16.0 at different Inlet Gas Void Fractions (IGVFs) and various flow rate values. Under conditions of IGVF = 0% (pure water) and IGVF = 15%, the accuracy of the numerical method was tested by comparing the experimental data. The results showed that the rotor–stator interaction was still the main generation driver of pressure fluctuation in gas–liquid two-phase pumps. However, the fluctuation near the impeller outlet ascribe to the rotor–stator interaction was weakened by the complex gas–liquid flow. For the different IGVF, the variation trend of fluctuation was similar along the streamwise direction. That is, the fluctuation in the impeller increased before decreasing, while in the guide vane it decreased gradually. Also, the fluctuation in the guide vane was generally greater than for the impeller and the maximum amplitude appeared in the vicinity of guide vane inlet

The effect of cooling rate on the wear performance of a ZrCuAlAg bulk metallic glass

In the present work, the local atomic ordering and the wear performance of ZrCuAlAg bulk metallic glass (BMG) samples with different diameters have been studied using transmission electron microscopy (TEM) plus autocorrelation function analysis, and pin-on-disc dry sliding wear experiments. Differential scanning calorimetry and TEM studies show that smaller diameter BMG sample has higher free volume and less local atomic ordering. The wear experiments demonstrate that with the same chemical composition, the smaller BMG sample exhibits higher coefficient of friction, higher wear rate, and rougher worn surface than those of the larger ones. Compared with larger BMG sample, the faster cooling rate of the smaller sample results in looser atomic configuration with more free volume, which facilitates the formation of the shear bands, and thus leads to larger plasticity and lower wear resistance. The results provide more quantitative understanding on the relationship among the cooling rate, the local atomic ordering, and the wear performance of BMGs

Mechanical properties and damage constitutive model of coal with different water content based on energy principle

In order to explore the energy evolution law and damage evolution characteristics of coal and rock mass in the process of deformation and failure under different water content, the uniaxial compression test of coal and rock mass in Shuangma No.1 Coal Mine under different water content conditions was carried out. Based on the principle of energy calculation and minimum energy consumption, the energy dissipation characteristics and damage evolution mechanism of coal and rock mass under different water content were analyzed. The results show that the mechanical properties of coal and rock mass under different water content are different, and the peak strain are positive correlated with water content, compressive strength and elastic modulus are negatively correlated with water content. The higher the water content of the coal and rock mass, the smaller the elastic strain energy at the peak value and the total strain energy absorbed by the failure, and the higher the proportion of the dissipated energy to the total strain energy. The damage constitutive model based on the principle of minimum energy consumption shows that the damage threshold value gradually decreases with the increase of water content of coal and rock mass. In the dry state, the damage variables of coal and rock mass at the peak stress are 0.36 and 0.28, respectively.When the water content increases to the natural state, the damage variables of coal and rock mass at the peak stress decrease by 0.09 and 0.18, respectively.However, when the water content increases to the saturated state, the damage variables of coal and rock mass at the peak stress increase by 0.102 and 0.49, respectively, showing a trend of decreasing first and then increasing.The evolution model of damage strain energy release rate of coal rock with different water content is further established. The maximum damage strain energy release rate of low water content coal rock is significantly lower than that of dry coal rock, and the decrease is 45.61% and 31.29% respectively. With the increase of water content to saturated state, the maximum damage strain energy release rate changes gently, which is 3.08% and 8.80% respectively, indicating that the damage severity of coal rock does not increase significantly

Numerical analysis of pressure fluctuation in a multiphase rotodynamic pump with air–water two-phase flow

Pressure fluctuation in single-phase pumps has been studied widely, while less attention has been paid to research on multiphase pumps that are commonly used in the petroleum chemical industry. Therefore, this study investigates the pressure fluctuation for a multiphase rotodynamic pump handling air–water two-phase flow. Simulations based on the Euler two-fluid model were carried out using ANSYS_CFX16.0 at different Inlet Gas Void Fractions (IGVFs) and various flow rate values. Under conditions of IGVF = 0% (pure water) and IGVF = 15%, the accuracy of the numerical method was tested by comparing the experimental data. The results showed that the rotor–stator interaction was still the main generation driver of pressure fluctuation in gas–liquid two-phase pumps. However, the fluctuation near the impeller outlet ascribe to the rotor–stator interaction was weakened by the complex gas–liquid flow. For the different IGVF, the variation trend of fluctuation was similar along the streamwise direction. That is, the fluctuation in the impeller increased before decreasing, while in the guide vane it decreased gradually. Also, the fluctuation in the guide vane was generally greater than for the impeller and the maximum amplitude appeared in the vicinity of guide vane inlet

Natural compounds in the management of polycystic ovary syndrome: a comprehensive review of hormonal regulation and therapeutic potential

Polycystic ovary syndrome (PCOS) is a multifaceted endocrine disorder characterized by irregularities in gonadotropin secretion, hyperandrogenism, chronic anovulation, and polycystic ovarian morphology. In addition, it is often associated with metabolic dysfunctions, most notably insulin resistance (IR). This disorder affects approximately 6–20% of individuals, primarily emerging during early adolescence, and considerably increases the risk of conditions such as impaired glucose tolerance, type 2 diabetes, endometrial cancer, cardiovascular diseases, dyslipidemia, and postpartum complications. To date, there is no standardized protocol for treating PCOS. Existing therapies primarily rely on personalized pharmacotherapy and lifestyle modifications. However, these treatments may often lead to adverse effects, and most medications prescribed for PCOS are used off-label and have not secured approval from the U.S. Food and Drug Administration specifically for this condition. Recently, natural compounds have garnered considerable attention due to their efficacy in hormone modulation and minimal toxicity. Substances such as myo-inositol, resveratrol, berberine, and quercetin have shown promise in mitigating PCOS symptoms. Their multi-target properties offer the potential to achieve outcomes unattainable by single-target pharmaceuticals, particularly in managing heterogeneous conditions. This review aims to comprehensively analyze in vivo and in vitro research alongside clinical interventions to evaluate the influence of natural compounds on the prevalence of PCOS and their therapeutic potential. These investigations lay the groundwork for developing innovative therapeutic strategies for PCOS

Gut microbiota influences feeding behavior via changes in olfactory receptor gene expression in Colorado potato beetles

The Colorado potato beetle (CPB) is an internationally recognized plant quarantine pest that causes serious losses to potato agricultural production. The gut microbiota plays an important role in its growth and development, and the olfactory system plays an important role in insect feeding behavior. The gut microbiota is known to be capable of inducing changes in the olfactory systems of insects. However, the way these associated gut microbes influence the feeding-related behaviors of CPBs remains unclear. To explore the relationship between them, fresh potato leaves immersed in a mixture of five antibiotics (tetracycline, penicillin, ofloxacin, ciprofloxacin, and ampicillin) at specific concentrations for 1 h were fed to adult CPBs to reduce the abundance of gut microbes. We found that the feeding behavior of CPBs was significantly affected by the gut microbiota and that Pseudomonas was significantly higher in abundance in the control group than in the antibiotic group. We then used transcriptome sequencing to explore the differences in olfactory receptor genes in the heads of non-treatment and antibiotic-fed CPBs. Through Illumina Hiseq™ sequencing and screening of differential genes, we found that the olfactory receptor gene LdecOR9 was significantly upregulated and LdecOR17 was significantly downregulated after antibiotic feeding. A real-time polymerase chain reaction was used to verify the changes in olfactory receptor gene expression in the non-treatment groups and antibiotic-treated groups. The feeding behavior was partially rescued after CPBs were re-fed with intestinal bacteria. These results indicate that a certain amount of gut microbiota can result in the loss of the olfactory discrimination ability of CPBs to host plants. In summary, this study investigated the relationship between gut microbiota and olfactory genes, providing a reference for research on microbial control

Expression pattern of NLRP3 and its related cytokines in the lung and brain of avian influenza virus H9N2 infected BALB/c mice

BACKGROUND: H9N2 avian influenza virus (AIV) becomes the focus for its ability of transmission to mammals and as a donor to provide internal genes to form the new epidemic lethal influenza viruses. Residue 627 in PB2 has been proven the virulence factor of H9N2 avian influenza virus in mice, but the detailed data for inflammation difference between H9N2 virus strains with site 627 mutation is still unclear. The inflammasome NLRP3 is recently reported as the cellular machinery responsible for activation of inflammatory processes and plays an important role during the development of inflammation caused by influenza virus infection. METHODS: In this study, we investigated the expression pattern of NLRP3 and its related cytokines of IL-1β and TNF-α in BALB/c mice infected by H9N2 AIV strains with only a site 627 difference at both mRNA and protein levels at different time points. RESULTS: The results showed that the expression level of NLRP3, IL-1β and TNF-α changed in the lung and brain of BALB/c mice after infection by V(K627) and rV(K627E). The immunohistological results showed that the positive cells of NLRP3, IL-1β and TNF-α altered the positive levels of original cells in tissues and infiltrated inflammatory cells which caused by H9N2 infection. CONCLUSIONS: Our results provided the basic data at differences in expression pattern of NLRP3 and its related cytokines in BALB/c mice infected by H9N2 influenza viruses with only a site 627 difference. This implied that NLRP3 inflammasome plays a role in host response to influenza virus infection and determines the outcome of clinical manifestation and pathological injury. This will explain the variable of pathological presentation in tissues and enhance research on inflammation process of the AIV H9N2 infection