A Note on the Maximum Genus of Graphs with Diameter 4

Let G be a simple graph with diameter four, if G does not contain complete subgraph K3 of order three

Singular perturbations for nonlinear Robin problems

AbstractIn this paper, taking the study of radially symmetric solutions for Poisson equation as the background, we discuss the existence, uniqueness and asymptotic estimates of solutions of the singularly perturbed Robin problem for the general nonlinear second-order ordinary differential equation with a small parameter ϵ > 0: a(x, ϵ) y″ = ƒ(x, y, y′, ϵ), 0 < x < 1, a0y(0, ϵ) − b0y′(0, ϵ) = A0, a1y(1, ϵ) + b1y′1(1, ϵ) = A1

Fundamental studies on poly(trimethylene terephthalate) spunbonded nonwovens

Spunbonding is the most productive of all the non-conventional methods of textile fabric formation. Isotactic polypropylene is the most widely used polymer in spunbonding production because it is the least expensive fiber-forming polymer that provides the highest yield. However, the main disadvantage of polypropylene is that it degrades in UV light or gamma radiation. With the increasing demand of the sterilized nonwovens, poly (trimethylene terephthalate) (PTT) has sparked an interest in this application due to its radiation resistance. In this research, we investigated the fundamental properties of PTT spunbonded nonwovens. The comparisons among PTT, PET and PP spunbonded nonwovens were conducted where appropriate. SEM was applied to examine the web structure. Web uniformity and fiber orientation analysis were conducted to study the web properties. The results showed that PTT spunbonded nonwovens have better elastic recovery and flexibility compared to PET and PP spunbonded nonwovens. PTT spunboned nonwovens are relatively thermal stable compared to PET and PP spunbonded nonwovens at high temperature (150°C)

HSP90 inhibitors stimulate DNAJB4 protein expression through a mechanism involving N6-methyladenosine.

Small-molecule inhibitors for the 90-kDa heat shock protein (HSP90) have been extensively exploited in preclinical studies for the therapeutic interventions of human diseases accompanied with proteotoxic stress. By using an unbiased quantitative proteomic method, we uncover that treatment with three HSP90 inhibitors results in elevated expression of a large number of heat shock proteins. We also demonstrate that the HSP90 inhibitor-mediated increase in expression of DNAJB4 protein occurs partly through an epitranscriptomic mechanism, and is substantially modulated by the writer, eraser, and reader proteins of N6-methyladenosine (m6A). Furthermore, exposure to ganetespib leads to elevated modification levels at m6A motif sites in the 5'-UTR of DNAJB4 mRNA, and the methylation at adenosine 114 site in the 5'-UTR promotes the translation of the reporter gene mRNA. This m6A-mediated mechanism is also at play upon heat shock treatment. Cumulatively, we unveil that HSP90 inhibitors stimulate the translation of DNAJB4 through an epitranscriptomic mechanism

Sensitive voltammetric detection of yeast RNA based on its interaction with Victoria Blue B

Voltammetric studies of the interaction of yeast RNA (y-RNA) with Victoria Blue B (VBB) are described in this paper. Furthermore, a linear sweep voltammetric method for the detection of y-RNA was established. The reaction conditions, such as acidity and amount of buffer solution, the concentration of VBB, the reaction time and temperature, etc., were carefully investigated by second order derivative linear sweep voltammetry. Under the optimal conditions, the reduction peak current of VBB at –0.75 V decreased greatly after the addition of y-RNA to the solution without any shift of the reduction peak potential. Based on the decrease of the peak current, a new quantitative method for the determination of y-RNA was developed. The effects of co-existing substances on the determination were carefully investigated and three synthetic samples were determined with satisfactory results. The stoichiometry of the VBB–y-RNA complex was calculated by linear sweep voltammetry and the interaction mechanism is discussed

Voltammetric determination of heparin based on its interaction with malachite green

In this paper malachite green (MG) was used as a bioprobe to determine heparin concentration by linear sweep voltammetry on the dropping mercury working electrode (DME). In Britton-Robinson (B-R) buffer solution of pH 1.5, MG had a well-defined second order derivative linear sweep voltammetric reductive peak at&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; &#8211;0.618 V (vs. SCE). After the addition of heparin into the MG solution, the reductive peak current decreased apparently without the movement of peak potential. Based on the difference of the peak current, a new voltammetric method for the determination of heparin was established. The conditions for the binding reaction and the electrochemical detection were optimized. Under the selected experimental conditions the difference of peak current was directly proportional to the concentration of heparin in the range from 0.3 to 10.0 mg/L with the linear regression equation as &#8710;ip&#8243; (nA) = 360.19 C (mg/L) + 178.88 (n = 15, &#947; = 0.998) and the detection limit as 0.28 mg/L (3&#963;). The effects of coexisting substances such as metal ions, amino acids on the determination of heparin were investigated and the results showed that this method had good selectivity. This method was further applied to determine the heparin content in heparin sodium injection samples with satisfactory results and good recovery. The stoichiometry of the biocomplex was calculated by the electrochemical method and the binding mechanism was further discussed.&#160;KEY WORDS: Heparin, Malachite green, Voltammetry, Binding reaction&#160;&#160;Bull. Chem. Soc. Ethiop. 2008, 22(2), 165-172

Shikra: Unleashing Multimodal LLM's Referential Dialogue Magic

In human conversations, individuals can indicate relevant regions within a scene while addressing others. In turn, the other person can then respond by referring to specific regions if necessary. This natural referential ability in dialogue remains absent in current Multimodal Large Language Models (MLLMs). To fill this gap, this paper proposes an MLLM called Shikra, which can handle spatial coordinate inputs and outputs in natural language. Its architecture consists of a vision encoder, an alignment layer, and a LLM. It is designed to be straightforward and simple, without the need for extra vocabularies, position encoder, pre-/post-detection modules, or external plug-in models. All inputs and outputs are in natural language form. Referential dialogue is a superset of various vision-language (VL) tasks. Shikra can naturally handle location-related tasks like REC and PointQA, as well as conventional VL tasks such as Image Captioning and VQA. Experimental results showcase Shikra's promising performance. Furthermore, it enables numerous exciting applications, like providing mentioned objects' coordinates in chains of thoughts and comparing user-pointed regions similarities. Our code and model are accessed at https://github.com/shikras/shikra

The Crossing Number of Two Cartesian Products

There are several known exact results on the crossing number of Cartesian products of paths, cycles, and complete graphs. In this paper, we find the crossing numbers of Cartesian products of Pn with two special 6-vertex graphs

Incoherent illumination for motion-based imaging through thick scattering medium

Object-motion-based speckle correlation can recover hidden objects from any inhomogeneous medium, which takes advantage of the inherent connection that the cross-correlation between speckle patterns can reflect the autocorrelation of object, providing a route for imaging through or inside thick scattering media. However, once the object is phase-modulated, the above-mentioned relation will not be satisfied under coherent illumination, and the objects cannot be recovered using the existing approaches. Here, we propose an incoherent illumination method for object-motion-based imaging. Theoretical analysis and experimental results show that the cross-correlation between the object-motion-based speckle patterns can be directly used to represent the intensity autocorrelation of the object, making it possible to recover hidden objects regardless of whether the object is phase-modulated or not. Moreover, the proposed approach has a lower root-mean-square error for extracting the autocorrelation patterns of the hidden object. The proposed imaging mechanism blazes a way of imaging moving objects with scattering-induced or intrinsic phase profile, which is in favor of complex imaging scenarios such as inhomogeneous object imaging, deep tissue imaging, and passive lighting scattering imaging