线性变换与其导数增长性比较的一个注记

研究了超越亚纯函数的分式线性变换的特征函数与其导数的特征函数增长性的比较，并由Ｎｅｖａｎｌｉｎｎａ理论推导出一个定理，其主要结果为：Ｔ（ｒ，Ｆ）＜４０λλ－１ｌｏｇｅλλ－１Ｔ（λｒ，ｆ′）＋ｌｏｇ＋（λｒ）＋ｌｏｇ＋｜ｆ（０）｜＋５＋ｌｏｇ＋ａｄ＋ｌｏｇ＋ｂｄ＋ｌｏｇ２（ｃ＝０）Ｔ（ｒ，Ｆ）＜４０λλ－１ｌｏｇｅλλ－１Ｔ（λｒ，Ｆ′）＋ｌｏｇ＋（λｒ）＋ｌｏｇ＋｜Ｆ（０）｜＋５＋ｌｏｇ＋ａｄ－ｂｃｃ２＋ｌｏｇ＋ｄｃ＋ｌｏｇ２＋ｈ（ｒ）（ｃ≠０）     

计算Kdv方程守恒密度的待定系数法

秩为ｒ的不可约单项式的集合Ｓｒ可以直接转化为Ｓ（ｒ＋１），多项式守恒密度Ｔ（ｒ＋１）＝Ｔ＿（ｒ＋１）￣０＋Ｕ＿（ｒ＋１），Ｔ＿（ｒ＋１）￣０的每一项都含因子ｕ＿０，可从Ｔ＿ｒ得到Ｕ＿（ｒ＋１）（ＣＳ＿（ｒ＋１））的每一项不含因子ｕ＿０，Ｕ＿（ｒ＋１）与Ｔ＿（ｒ＋１）￣０的项之间存在着特殊的相关性，由此可分批求出Ｕ＿（ｒ＋１）中的特定系数且不涉及Ｘ＿（ｒ＋１）。     

一个连续勾股数的构造定理

如果（ｎ＋１）￣２＋（ｎ＋２）￣２＋…＋（ｎ＋ｋ）￣２＝（ｎ＋ｋ＋１）￣２＋（ｎ＋ｋ＋２）￣２＋…＋（ｎ＋２ｋ－ｍ）￣２，则称ｎ＋１，ｎ＋２，…，ｎ十ｋ，ｎ＋ｋ＋１，…，ｎ＋２ｋ－ｍ为一组ｍ类连续勾股数．给出了寻找ｍ类连续勾股数的一种方法．并由此得到了下列结果：１．ｍ＝１时，连续勾股数只有已知的唯一形式（ｎ＝１，２，３，…）：（２ｎ￣２＋ｎ）￣２＋（２ｎ￣２＋ｎ＋１）￣２＋…＋（２ｎ￣２＋２ｎ）￣２＝（２ｎ￣２＋２ｎ＋１）￣２＋…＋（２ｎ￣２＋３ｎ）￣２２．下列的ｍ类连续勾股数不存在：ｍ≡３（ｍｏｄ８），ｍ≡４（ｍｏｄ８），ｍ≡５（ｍｏｄ８）．３．当２≤ｍ≤１００时，只有６组ｍ类连续勾股数．还给出了一个连续勾股数的构造定理，由此可导出一系列ｋ＝ｔｍ型的连续勾股数．     

球面稳定同伦群的一族新元素g0(b1)2(γ～)s

证明了在经典Adams谱序列中，当P≥11，3≤s≤P-3时，g0（b1）^2∈ExtA^6,2p^2q＋pq＋2q（H＊V（2）,Zp）在，Adams谱序列中收剑到π2p^2q＋pq＋2q-V（2）的非零元，g0（b1）^2γ，∈ExtA^6＋s,（s＋2）p^2q＋spq＋sq＋（s-3）（Zp,Zp）在Adams谱序列中收剑到π（s＋2）p^2q＋spq＋sq-9S的非零元。     

一类新算子的同时逼近

引入一种新的正线性算子并研究它对于无界函数的同时逼近.设ｆ∈Ｃβ[０，∞），ｒ∈N，ｆ（ｘ）在[０，∞）存在ｒ阶导数，则ｌｉｍｎ∞Ｍ（ｒ）ｎ，α（ｆ（ｔ），ｘ）＝ｆ（ｒ）（ｘ）；若ｆ（ｒ）（ｘ）∈Ｃ（ａ－η，ｂ＋η）（η＞０），则Ｍ（ｒ）ｎ，α（ｆ，ｘ）ｆ（ｒ）（ｘ）在ｘ∈[ａ，ｂ]一致成立.设ｆ∈Ｃβ[０，∞），ｆ（ｘ）在[０，∞）上存在ｒ＋２阶导数，则ｌｉｍｎ∞ｎ[Ｍ（ｒ）ｎ，α（ｆ，ｘ）－ｆ（ｒ）（ｘ）]＝α[ｒ（ｒ＋１）ｆ（ｒ）（ｘ）＋（２（ｒ＋１）ｘ＋ｒ）ｆ（ｒ＋１）（ｘ）＋ｘ（１＋ｘ）ｆ（ｒ＋２）（ｘ）]；若ｆ（ｒ＋２）（ｘ）∈Ｃａ－η，ｂ＋η）（η＞０），则上式在[ａ，ｂ]一致成立.     

钙在植物盐毒害中的作用

盐毒害作用包括渗透胁迫和离子胁迫两大类，它们都能严重影响根系和新稍的生长。Ｎａ~＋减少了质膜对Ｃａ~（＋＋）的束缚，当Ｃａ~（＋＋）向外流出增加时，Ｎａ~＋能抑制Ｃａ~（＋＋）进入胞内，并耗尽内质膜上的Ｃａ~（＋＋），这些变化表明，Ｃａ~（＋＋）的变化是根系细胞受到盐胁迫后的原初反应。盐能很快减少Ｃａ~（＋＋）向叶细胞的转运，Ｎａ~＋干扰了根系细胞内Ｃａ~（＋＋）的平衡，盐胁迫时补Ｃａ~（＋＋）能产生良好作用。     

磺化乙丙三元胶固体中离子相互作用的研究

合成了分别含Ｌｉ￣＋，Ｎａ￣＋，Ｋ￣＋和Ｍｇ￣（２＋），Ｃａ￣（２＋），Ｂａ￣（２＋）的６种乙丙三元胶（ＥＰＤＭ）磺酸盐离聚体，溶解性试验反映出固体中存在聚集引起的离子交联，红外光谱表明金属离子与的相互作用为Ｌｉ￣＋＞Ｎａ￣＋＞Ｋ￣＋和Ｍｇ￣（２＋）＞Ｃａ￣（２＋）＞Ｂａ￣（２＋）及Ｍ￣（２＋）＞Ｍ￣＋，通过动态力学分析，讨论了离聚体中离子相互作用对离子聚集和橡胶平台区温度范围的影响规律。     

一类时滞微分方程正解的存在性

研究一类一阶非线性时滞微分方程，x′（t）＋a（r）f（x（t））＋p（t）g（x（t））h（x（t-τ1（t）），x（t-τ2（t）），…，x（t-τn（t）））=0，其中，a,p，τj∈C（R^＋，R^＋），limt→＋∞（t-τ1（t））=＋∞，j=1，2，…，n，f，g∈C（R，R），获得了其存在正解的充分条件。     

非线性具偏差变元的时超泛函微分方程解的振动性

本文研究了一阶非线性具偏差变元的超前型泛函微分方程：ｘ（ｔ）＝ａ（ｔ）∏ｍｉ＝１［ｘ（ｔ＋ｒｊ（ｔ））］αｊ（＊）及ｘ（ｔ）＝ａ（ｔ）ｆ［ｘ（ｔ＋ｒ１（ｔ）），ｘ（ｔ＋ｒ２（ｔ）），…，ｘ（ｔ＋ｒｍ（ｔ）］＋ｇ［ｔ，ｘ（ｔ），ｘ（ｔ＋ｒ１（ｔ）），…，ｘ（ｔ＋ｒｍ（ｔ））］（＊＊）解的振动性问题，给出了方程（＊）与（＊＊）解振动的充分条件     

（Y，Ce，Sm）（Mg，Mn）B_5O_（10）中Sm~（3＋）的发光与Mn~

研究了（Ｙ，Ｃｅ，Ｓｍ）（Ｍｇ，Ｍｎ）Ｂ５Ｏ（１０）中Ｓｍ（３＋）和Ｍｎ（２＋）的发光性质，Ｍｎ（２＋）浓度对Ｓｍ（３＋）发射的影响．着重讨论了Ｍｎ（２＋）对Ｓｍ（３＋）发射的敏化作用及能量传递机理．     

蚯蚓钙调素结合蛋白的研究

以赤子爱胜蚓(Eisenia Foetida)为材料,通过DEAE-Fast Flow离子交换层析、CaM-Sepharose亲和层析,分离纯化得到蚯蚓钙调素结合蛋白(CaMBPs)。纯化的CaMBPs对CaM激活的环核苷酸磷酸二酯酶活性有抑制作用,而且这种抑制作用可通过加入过量的CaM达到完全恢复。SDS-PAGE显示CaMBPs有3条明显主带,在EGTA存在时表现分子量分别为62, 49和30kD。紫外扫描测定含量分别为7.17%,7.31%和51.8%。用生物素-CaM覆盖法检测到3种CaM结合蛋白,与SDS-PAGE结果一致。酶活性测定实验表明在蚯蚓CaMBPs中有Ca²⁺-ATPase活性,但无NAD激酶活性。     

Fluorescence Spectra Studies on the Interaction between Lanthanides and Calmodulin

ＩｎｔｒｏｄｕｃｔｉｏｎＬａｎｔｈａｎｉｄｅ (Ｌｎ3 )ｃａｎ ｐｒｏｍｏｔｅｔｈｅｇｒｏｗｔｈｏｆｃｒｏｐｓａｎｄｉｎｃｒｅａｓｅｔｈｅｉｒｐｒｏｄｕｃｔｉｏｎ .Ｈｏｗｅｖｅｒ ,Ｌｎ3 ｃａｎａｌｓｏａｆｆｅｃｔａｎｉｍａｌｔｉｓｓｕｅｓａｎｄｈａｓｓｏｍｅｔｏｘｉｃｆｕｎｃｔｉｏｎｓａｔｃｅｒｔａｉｎｃｏｎｃｅｎｔｒａｔｉｏｎｓ[1] .ＴｈｅｍｅｃｈａｎｉｓｍｂｙｗｈｉｃｈＬｎ3 ｅｘｅｒｔｓｂｉｏｌｏｇｉｃａｌｅｆｆｅｃｔｓｒｅｍａｉｎｓｕｎｃｌｅａｒ.ＳｔｕｄｉｅｓｓｈｏｗｔｈａｔＬｎ3 ｃａｎｉ…     

Ca~（2＋）和亚精胺在莴苣种子萌发过程中的相互关系

莴苣（挂丝红品种）种子萌发过程中，内源亚精胺（Ｓｐｄ）含量逐渐增加．Ｃａ２＋通道抑制剂Ｃｏ２＋和Ｌ３＋、钙调素（ＣａＭ）拮抗剂氯两嗪（ＣＰＺ）处理抑制种子内源亚精胺含量的增加，Ｃａ２＋可部分逆转Ｃｏ２＋和Ｌａ３＋的抑制效应．外源亚精胺处理能部分逆转Ｃｏ２＋和Ｌａ３＋对萌发的抑制效应．表明Ｃａ２＋和ＣａＭ对种子萌发的调节作用与其对亚精胺含量的影响有关．     

Structure of the gating domain of a Ca2+-activated K+ channel complexed with Ca2+/calmodulin

Small-conductance Ca2+-activated K+ channels (SK channels) are independent of voltage and gated solely by intracellular Ca2+. These membrane channels are heteromeric complexes that comprise pore-forming alpha-subunits and the Ca2+-binding protein calmodulin (CaM). CaM binds to the SK channel through the CaM-binding domain (CaMBD), which is located in an intracellular region of the alpha-subunit immediately carboxy-terminal to the pore. Channel opening is triggered when Ca2+ binds the EF hands in the N-lobe of CaM. Here we report the 1.60 A crystal structure of the SK channel CaMBD/Ca2+/CaM complex. The CaMBD forms an elongated dimer with a CaM molecule bound at each end; each CaM wraps around three alpha-helices, two from one CaMBD subunit and one from the other. As only the CaM N-lobe has bound Ca2+, the structure provides a view of both calcium-dependent and -independent CaM/protein interactions. Together with biochemical data, the structure suggests a possible gating mechanism for the SK channel.     

Effect of La^3＋ on myocardiac potassium channels revealed by patch-clamp technique

The effect of La^3 on potassium channels in rat ventricular myocytes was investigated using the whole-cell patch-clamp recording mode. The Ca^2 -independent voltage-activated outward K~ current was activated by the depolar-izing pulse in enzymatically isolated rat ventricular myocytes. After addition of different concentrations La^3 to the bath solution, the outward K^ current was depressed gradually. The inhibition effect was in a concentration-dependent manner. The phenomena of the outward K^ current, being themain repolarizing current suppressed by La^3 , suggest that the effect of lanthanides on myocardial function should be exploited further.     

Calmodulin bifurcates the local Ca2+ signal that modulates P/Q-type Ca2+ channels

Acute modulation of P/Q-type (alpha1A) calcium channels by neuronal activity-dependent changes in intracellular Ca2+ concentration may contribute to short-term synaptic plasticity, potentially enriching the neurocomputational capabilities of the brain. An unconventional mechanism for such channel modulation has been proposed in which calmodulin (CaM) may exert two opposing effects on individual channels, initially promoting ('facilitation') and then inhibiting ('inactivation') channel opening. Here we report that such dual regulation arises from surprising Ca2+-transduction capabilities of CaM. First, although facilitation and inactivation are two competing processes, both require Ca2+-CaM binding to a single 'IQ-like' domain on the carboxy tail of alpha1A; a previously identified 'CBD' CaM-binding site has no detectable role. Second, expression of a CaM mutant with impairment of all four of its Ca2+-binding sites (CaM1234) eliminates both forms of modulation. This result confirms that CaM is the Ca2+ sensor for channel regulation, and indicates that CaM may associate with the channel even before local Ca2+ concentration rises. Finally, the bifunctional capability of CaM arises from bifurcation of Ca2+ signalling by the lobes of CaM: Ca2+ binding to the amino-terminal lobe selectively initiates channel inactivation, whereas Ca2+ sensing by the carboxy-terminal lobe induces facilitation. Such lobe-specific detection provides a compact means to decode local Ca2+ signals in two ways, and to separately initiate distinct actions on a single molecular complex.     

A calcium sensor in the sodium channel modulates cardiac excitability.

Sodium channels are principal molecular determinants responsible for myocardial conduction and maintenance of the cardiac rhythm. Calcium ions (Ca2+) have a fundamental role in the coupling of cardiac myocyte excitation and contraction, yet mechanisms whereby intracellular Ca2+ may directly modulate Na channel function have yet to be identified. Here we show that calmodulin (CaM), a ubiquitous Ca2+-sensing protein, binds to the carboxy-terminal 'IQ' domain of the human cardiac Na channel (hH1) in a Ca2+-dependent manner. This binding interaction significantly enhances slow inactivation-a channel-gating process linked to life-threatening idiopathic ventricular arrhythmias. Mutations targeted to the IQ domain disrupted CaM binding and eliminated Ca2+/CaM-dependent slow inactivation, whereas the gating effects of Ca2+/CaM were restored by intracellular application of a peptide modelled after the IQ domain. A naturally occurring mutation (A1924T) in the IQ domain altered hH1 function in a manner characteristic of the Brugada arrhythmia syndrome, but at the same time inhibited slow inactivation induced by Ca2+/CaM, yielding a clinically benign (arrhythmia free) phenotype.     

Regulation of Ca2+ channel expression at the cell surface by the small G-protein kir/Gem

Voltage-dependent calcium (Ca2+) channels are involved in many specialized cellular functions, and are controlled by intracellular signals such as heterotrimeric G-proteins, protein kinases and calmodulin (CaM). However, the direct role of small G-proteins in the regulation of Ca2+ channels is unclear. We report here that the GTP-bound form of kir/Gem, identified originally as a Ras-related small G-protein that binds CaM, inhibits high-voltage-activated Ca2+ channel activities by interacting directly with the beta-subunit. The reduced channel activities are due to a decrease in alpha1-subunit expression at the plasma membrane. The binding of Ca2+/CaM to kir/Gem is required for this inhibitory effect by promoting the cytoplasmic localization of kir/Gem. Inhibition of L-type Ca2+ channels by kir/Gem prevents Ca2+-triggered exocytosis in hormone-secreting cells. We propose that the small G-protein kir/Gem, interacting with beta-subunits, regulates Ca2+ channel expression at the cell surface.     

乙酰胆碱酯酶与新型香豆素类二聚体抑制剂的作用研究

本文通过分子对接的方法研究了香豆素类二聚体作为AChE抑制剂在正常活性位点（Set203、Glu334和His447）和外周阴离子活性位点（His287、Tyr72、Tyr441和Glu292）的作用情况．研究结果表明，此类抑制剂有两个负电性中心：抑制剂母体的内酯区和6位或7位的苄基区．由于这两部分负电作用比较强极易与周围蛋白质发生静电作用，从而导致氢键的形成．研究发现香豆素二聚体类抑制剂更容易结合在AChE的外周阴离子活性区域．这类抑制剂在外周阴离子活性位点有相同的作用模式．这使得香豆素类二聚体有可能成为一种有更好应用前景的乙酰胆碱酯酶抑制剂．     

A modular switch for spatial Ca2+ selectivity in the calmodulin regulation of CaV channels

Ca2+/calmodulin-dependent regulation of voltage-gated CaV1-2 Ca2+ channels shows extraordinary modes of spatial Ca2+ decoding and channel modulation, vital for many biological functions. A single calmodulin (CaM) molecule associates constitutively with the channel's carboxy-terminal tail, and Ca2+ binding to the C-terminal and N-terminal lobes of CaM can each induce distinct channel regulations. As expected from close channel proximity, the C-lobe responds to the roughly 100-microM Ca2+ pulses driven by the associated channel, a behaviour defined as 'local Ca2+ selectivity'. Conversely, all previous observations have indicated that the N-lobe somehow senses the far weaker signals from distant Ca2+ sources. This 'global Ca2+ selectivity' satisfies a general signalling requirement, enabling a resident molecule to remotely sense cellular Ca2+ activity, which would otherwise be overshadowed by Ca2+ entry through the host channel. Here we show that the spatial Ca2+ selectivity of N-lobe CaM regulation is not invariably global but can be switched by a novel Ca2+/CaM-binding site within the amino terminus of channels (NSCaTE, for N-terminal spatial Ca2+ transforming element). Native CaV2.2 channels lack this element and show N-lobe regulation with a global selectivity. On the introduction of NSCaTE into these channels, spatial Ca2+ selectivity transforms from a global to local profile. Given this effect, we examined CaV1.2/CaV1.3 channels, which naturally contain NSCaTE, and found that their N-lobe selectivity is indeed local. Disruption of this element produces a global selectivity, confirming the native function of NSCaTE. Thus, differences in spatial selectivity between advanced CaV1 and CaV2 channel isoforms are explained by the presence or absence of NSCaTE. Beyond functional effects, the position of NSCaTE on the channel's amino terminus indicates that CaM can bridge the amino terminus and carboxy terminus of channels. Finally, the modularity of NSCaTE offers practical means for understanding the basis of global Ca2+ selectivity.