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# Complete monotonicity of two functions involving the tri-and tetra-gamma functions

Periodica Mathematica Hungarica
Authors: Jiao-Lian Zhao, Bai-Ni Guo, and Feng Qi

## Abstract

The psi function ψ(x) is defined by ψ(x) = Γ′(x)/Γ(x) and ψ (i)(x), for i ∈ ℕ, denote the polygamma functions, where Γ(x) is the gamma function. In this paper, we prove that the functions
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$[\psi '(x)]^2 + \psi ''(x) - \frac{{x^2 + 12}} {{12x^4 (x + 1)^2 }}$$ \end{document}
and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{{x + 12}} {{12x^4 (x + 1)}} - \{ [\psi '(x)]^2 + \psi ''(x)\}$$ \end{document}
are completely monotonic on (0,∞).
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# Synthesis and biodistribution of 99mTc-peptides conjugated adenine as tumor imaging agents

Journal of Radioanalytical and Nuclear Chemistry
Authors: Y. Zhao, C. Zhang, C. Qi, S. Feng, G. You, Z. Fu, F. Guo, and R. Wang

## Abstract

Two peptide ligands conjugated adenine, [9-N-(tritylmercapto acetyl diglycyl aminoethyl) adenine, Tr-MAG2-Ade] and [9-N-(tritylmercapto acetyl triglycyl aminoethyl) adenine, Tr-MAG3-Ade], are synthesized and labeled with 99mTc by directly labeling method. The stability of 99mTc-MAG2-adenine and 99mTc-MAG3-adenine in vitro is measured. The uptake radios of tumor to muscle at 3h post-injection are 5.70 and 4.92, respectively. The biodistribution and scintigraphic imaging studies show that the two complexes have high localization in tumor and high contrasted tumor images can be obtained, which suggest their potential utility as tumor imaging agents. But the high radioactivity of abdomen could prevent the tumor imaging in this area.

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# Biodistribution and imaging of 99mTc-MAVGG-adenine in tumor bearing mice

Journal of Radioanalytical and Nuclear Chemistry
Authors: C. Zhang, Y. Zhao, S. Feng, C. Qi, Z. Fu, F. Guo, and R. Wang

## Abstract

To increase the tumor uptake of Val-Gly-Gly (VGG), adenine was introduced into the peptide. N-mercaptoacetyl-VGG-adenine (MAVGG-adenine) and MAVGG were labeled with 99mTc using a solution of SnCl2 and tartaric acid as reducing agent. Biodistribution in mice bearing the S180 tumor was measured and γ imaging was performed. Compared with MAVGG, adenine conjugated MAVGG had higher tumor uptake and tumor to normal tissue ratios, which suggested that the tumor uptake property of a peptide may be improved by introducing a nucleotide base. The high contrasted tumor images of 99mTc-MAVGG-adenine also suggested its potential utility as tumor imaging agent.

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# Synthesis and thermal behavior of 4,5-dihydroxyl-2-(dinitromethylene)-imidazolidine (DDNI)

Journal of Thermal Analysis and Calorimetry
Authors: Kang-Zhen Xu, Yong-Shun Chen, Min Wang, Jin-An Luo, Ji-Rong Song, Feng-Qi Zhao, and Rong-Zu Hu

## Abstract

A novel energetic material, 4,5-dihydroxyl-2-(dinitromethylene)-imidazolidine (DDNI), was synthesized by the reaction of FOX-7 and glyoxal in water at 70 °C. Thermal behavior of DDNI was studied with DSC and TG-DTG methods, and presents only an intense exothermic decomposition process. The apparent activation energy and pre-exponential factor of the decomposition reaction were 286.0 kJ mol−1 and 1031.16 s−1, respectively. The critical temperature of thermal explosion of DDNI is 183.78 °C. Specific heat capacity of DDNI was studied with micro-DSC method and theoretical calculation method, and the molar heat capacity is 217.76 J mol−1 K−1 at 298.15 K. The adiabatic time-to-explosion was also calculated to be a certain value between 14.54 and 16.34 s. DDNI presents lower thermal stability, for its two ortho-hydroxyl groups, and its thermal decomposition process becomes quite intense.

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# Thermal decomposition mechanism and quantum chemical investigation of hydrazine 3-nitro-1,2,4-triazol-5-one (HNTO)

Journal of Thermal Analysis and Calorimetry
Authors: Jian-Hua Yi, Feng-Qi Zhao, Ying-Hui Ren, Si-Yu Xu, Hai-Xia Ma, and Rong-Zu Hu

## Abstract

The thermal decomposition mechanism of hydrazine 3-nitro-1,2,4-triazol-5-one (HNTO) compound was studied by means of differential scanning calorimetry (DSC), thermogravimetry and derivative thermogravimetry (TG-DTG), and the coupled simultaneous techniques of in situ thermolysis cell with rapid scan Fourier transform infrared spectroscopy (in situ thermolysis/RSFTIR). The thermal decomposition mechanism is proposed. The quantum chemical calculation on HNTO was carried out at B3LYP level with 6-31G+(d) basis set. The results show that HNTO has two exothermic decomposition reaction stages: nitryl group break first away from HNTO molecule, then hydrazine group break almost simultaneously away with carbonyl group, accompanying azole ring breaking in the first stage, and the reciprocity of fragments generated from the decomposition reaction is appeared in the second one. The C–N bond strength sequence in the pentabasic ring (shown in Scheme 1) can be obtained from the quantum chemical calculation as: C3–N4 > N2–C3 > N4–C5 > N1–C5. The weakest bond in NTO is N7–C3. N11–N4 bond strength is almost equal to N4–C5. The theoretic calculation is in agreement with that of the thermal decomposition experiment.

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# Thermochemical properties of di(N,N-di(2,4,6-trinitrophenyl)amino)-ethylenediamine in dimethyl sulfoxide and N-methyl pyrrolidone

Journal of Thermal Analysis and Calorimetry
Authors: Li Bai Xiao, Xiao Ling Xing, Xue Zhong Fan, Feng Qi Zhao, Zhi Ming Zhou, Hai Feng Huang, Ting An, Hai Xia Hao, and Qing Pei

## Abstract

The enthalpies of dissolution for di(N,N-di(2,4,6,-trinitrophenyl)amino)-ethylenediamine (DTAED) in dimethyl sulfoxide (DMSO) and N-methyl pyrrolidone (NMP) were measured using a RD496-2000 Calvet microcalorimeter at 298.15 K. Empirical formulae for the calculation of the enthalpies of dissolution (Δdiss H) were obtained from the experimental data of the dissolution processes of DTAED in DMSO and NMP. The linear relationships between the rate (k) and the amount of substance (a) were found. The corresponding kinetic equations describing the two dissolution processes were for the dissolution of DTAED in DMSO, and for the dissolution of DTAED in NMP, respectively.

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# BTATz-CMDB propellants

## High-pressure thermal properties and their correlation with burning rates

Journal of Thermal Analysis and Calorimetry
Authors: Jian-Hua Yi, Feng-Qi Zhao, Ying-Hui Ren, Bo-Zhou Wang, Cheng Zhou, Xiao-Ning Ren, Si-Yu Xu, Hai-Xia Hao, and Rong-Zu Hu

## Abstract

The high-pressure thermal properties and their correlation with burning rates of the composite modified double base (CMDB) propellants containing 3,6-bis (1H-1,2,3,4-tetrazol-5-yl-amino)-1,2,4,5-tetrazine (BTATz), a substitute of hexogen (RDX), were investigated using the high-pressure differential scanning calorimetry (PDSC). The results show that there is a main exothermal decomposition process with the heating of each propellant. High pressure can restrain the volatilization of NG, accelerate the main decomposition reaction, and make the reaction occur easily. High pressure can change the main decomposition reaction mechanism function and kinetics, and the control process obeys the rule of Avrami–Erofeev equation at high pressure and chemical reaction at normal pressure. However, the mechanism function can not be changed by the ballistic modifier. The correlation between PDSC characteristic values and burning rates was carried out and found that u and keep a good linear relation, k u keeps a similar changing trend with u, and it can be used to study the effect of the ballistic modifier or the other component on the burning rates.

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# Thermal behavior of 3,4,5-triamino-1,2,4-triazole dinitramide

Journal of Thermal Analysis and Calorimetry
Authors: Liang Xue, Feng-Qi Zhao, Xiao-Ling Xing, Zhi-Ming Zhou, Kai Wang, Hong-Xu Gao, Jian-Hua Yi, and Rong-Zu Hu

## Abstract

The thermal decomposition behavior of 3,4,5-triamino-1,2,4-triazole dinitramide was measured using a C-500 type Calvet microcalorimeter at four different temperatures under atmospheric pressure. The apparent activation energy and pre-exponential factor of the exothermic decomposition reaction are 165.57 kJ mol−1 and 1018.04s−1, respectively. The critical temperature of thermal explosion is 431.71 K. The entropy of activation (ΔS ), enthalpy of activation (ΔH ), and free energy of activation (ΔG ) are 97.19 J mol−1K−1, 161.90 kJ mol−1, and 118.98 kJ mol−1, respectively. The self-accelerating decomposition temperature (T SADT) is 422.28 K. The specific heat capacity of 3,4,5-triamino-1,2,4-triazole dinitramide was determined with a micro-DSC method and a theoretical calculation method. Specific heat capacity (J g−1K−1) equation is C p = 0.252 + 3.131 × 10−3 T (283.1 K < T < 353.2 K). The molar heat capacity of 3,4,5-triamino-1,2,4-triazole dinitramide is 264.52 J mol−1 K−1 at 298.15 K. The adiabatic time-to-explosion of 3,4,5-triamino-1,2,4-triazole dinitramide is calculated to be a certain value between 123.36 and 128.56 s.

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# Thermal behavior of 1,2,3-triazole nitrate

Journal of Thermal Analysis and Calorimetry
Authors: Liang Xue, Feng-Qi Zhao, Xiao-Ling Xing, Zhi-Ming Zhou, Kai Wang, Hong-Xu Gao, Jian-Hua Yi, Si-Yu Xu, and Rong-Zu Hu

## Abstract

The thermal decomposition behaviors of 1,2,3-triazole nitrate were studied using a Calvet Microcalorimeter at four different heating rates. Its apparent activation energy and pre-exponential factor of exothermic decomposition reaction are 133.77 kJ mol−1 and 1014.58 s−1, respectively. The critical temperature of thermal explosion is 374.97 K. The entropy of activation (ΔS ), the enthalpy of activation (ΔH ), and the free energy of activation (ΔG ) of the decomposition reaction are 23.88 J mol−1 K−1, 130.62 kJ mol−1, and 121.55 kJ mol−1, respectively. The self-accelerating decomposition temperature (T SADT) is 368.65 K. The specific heat capacity was determined by a Micro-DSC method and a theoretical calculation method. Specific heat capacity equation is (283.1 K < T < 353.2 K). The adiabatic time-to-explosion is calculated to be a certain value between 98.82 and 100.00 s. The critical temperature of hot-spot initiation is 637.14 K, and the characteristic drop height of impact sensitivity (H 50) is 9.16 cm.

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# Synthesis and thermal behavior of a new high-energy organic potassium salt

## K(AHDNE)

Journal of Thermal Analysis and Calorimetry
Authors: Kang-Zhen Xu, Xian-Gang Zuo, Hang Zhang, Biao Yan, Jie Huang, Hai-Xia Ma, Bo-Zhou Wang, and Feng-Qi Zhao

## Abstract

A new high-energy organic potassium salt, 1-amino-1-hydrazino-2,2-dinitroethylene potassium salt [K(AHDNE)], was synthesized by reacting of 1-amino-1-hydrazino-2,2-dinitroethylene (AHDNE) and potassium hydroxide in methanol aqueous solution. The thermal behavior of K(AHDNE) was studied using DSC and TG/DTG methods and can be divided into three obvious exothermic decomposition processes. The decomposition enthalpy, apparent activation energy and pre-exponential factor of the first decomposition process were −2662.5 J g−1, 185.2 kJ mol−1 and 1019.63 s−1, respectively. The critical temperature of thermal explosion of K(AHDNE) is 171.38 °C. The specific heat capacity of K(AHDNE) was determined using a micro-DSC method, and the molar heat capacity is 208.57 J mol−1 K−1 at 298.15 K. Adiabatic time-to-explosion of K(AHDNE) was also calculated. K(AHDNE) presents higher thermal stability than AHDNE.

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