A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture

This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.

Synthesis, Crystal Structure, Fluorescent Property and DFT Calculations of a New Zn(Ⅱ) Complex Based on 3-(2-Pyridyl)-5-(4-pyridyl)-1H-1,2,4-triazole

A new coordination compound Zn（2,4＇-bpt）2（H2O）（1） based on the versatile ligand 2,4＇-Hbpt（2,4？-Hbpt = 3-（2-pyridyl）-5-（4-pyridyl）-1H-1,2,4-triazole） was prepared by hydrothermal reactions. The structure of complex 1 has been characterized by X-ray single-crystal diffraction, elemental analysis, X-ray powder diffraction, IR spectrum analysis and thermogravimetric analysis. Single-crystal X-ray diffraction analysis indicates that the complex belongs to monoclinic system, space group C2/c with a = 23.877（3）, b = 0.7483（9）, c = 1.2492（2） A, b = 92.681（2）°, V = 2230.6（4） A^3, Z = 4, Dc = 1.572 g/cm^3, m = 1.143 mm^-1, Mr = 527.85 and F（000） = 1080. The final R = 0.0581 and wR = 0.0898 with I 〉 2s（I）. 1 is a 0D motif which is connected by hydrogen bonds to form a corrugated 1D pattern. In addition, 1 shows strong photoluminescent emissions in the solid state at room temperature which can be used as potential optical materials. Theoretical calculations based on density functional theory（DFT） were employed in order to explicate the stability and chemical reactivity of 2,4＇-Hbpt with different conformations. The results indicated that conformation I is more stable and prior to coordination in the reactions.

On the road towards the global analysis of human synapses

Synapses are essential units for the flow of information in the brain.Over the last 70 years,synapses have been widely studied in multiple animal models including worms,fruit flies,and rodents.In comparison,the study of human synapses has evolved significantly slower,mainly because of technical limitations.However,three novel methods allowing the analysis of molecular,morphological,and functional properties of human synapses may expand our knowledge of the human brain.Here,we briefly describe these methods,and evaluate how the information provided by each unique approach may contribute to the functional and anatomical analysis of the synaptic component of human brain circuitries.In particular,using tissue from cryopreserved human brains,synaptic plasticity can be studied in isolated synaptosomes by fluorescence analysis of single-synapse long-term potentiation（FASS-LTP）,and subpopulations of synapses can be thoroughly assessed in the ribbons of brain tissue by array tomography（AT）.Currently,it is also possible to quantify synaptic density in the living human brain by positron emission tomography（PET）,using a novel synaptic radio-ligand.Overall,data provided by FASS-LTP,AT,and PET may significantly contribute to the global understanding of synaptic structure and function in both healthy and diseased human brains,thus directly impacting translational research.

1-(3-Aminopropyl)-3-butylimidazolium bromide for carboxyl group derivatization:potential applications in high sensitivity peptide identification by mass spectrometry

The cationic reagent 1-(3-aminopropyl)-3-butylimidazolium bromide(BAPI) was exploited for the derivatization of carboxyl groups on peptides.Nearly 100% derivatization efficiency was achieved with the synthetic peptide RVYVHPI(RI-7).Furthermore,the peptide derivative was stable in a 0.1% TFA/water solution or a 0.1%(v/v) TFA/acetonitrile/water solution for at least one week.The effect of BAPI derivatization on the ionization of the peptide RI-7 was further investigated,and the detection sensitivity was improved >42-fold via matrix-assisted laser desorption/ionization time-of-flight mass spectrometry(MALDI-TOF MS),thus outperforming the commercial piperazine derivatization approach.Moreover,the charge states of the peptide were largely increased via BAPI derivatization by electrospray ionization(ESI) MS.The results indicate the potential merits of BAPI derivatization for high sensitivity peptide analysis by MS.

A New Co(Ⅱ)Coordination Compound Constructed by Tripyridyltriazole and Pyromellitic Acid:Synthesis,Crystal Structure and Antifungal Activity

A new coordination compound, [Co（L223）2（H2O）2]·H2pm（1, L223 = 3,4-bis（2-pyridyl）-5-（3-pyridyl）-1,2,4-triazole and H4 pm = pyromellitic acid）, has been synthesized. The structure of complex 1 has been characterized by X-ray single-crystal diffraction, elemental analysis, IR spectrum analysis and thermogravimetric analysis. Single-crystal X-ray diffraction analysis reveals that complex 1 belongs to the triclinic system, space group P1 with a = 10.2470（8）, b = 10.2879（9）, c = 10.2951（11） ？, α = 109.398（2）, β = 97.6590（10）, γ = 95.3260（10）°, V = 1003.60（16） ？3, Z = 1, Dc = 1.565 g/cm^3, μ = 0.508 mm%^-1, Mr = 945.73, F（000） = 485, the final R = 0.0562 and w R = 0.0783 with I 〉 2σ（I）. Two L223 as chelating ligands link one Co（II） ion to form a 0D motif. Furthermore, the 0D motifs are linked into a 2D coordination pattern with hydrogen bonds. In addition, the antifungal effects of the ligand and the complex were evaluated by the disc diffusion method against Colletotrichum gloeosporioides Penz. 1 represents antifungal activity with high levels of inhibitory potency which is larger than the corresponding ligand.