一种求1∞型未定式极限的简便方法

两个重要极限是《高等数学》中求极限的主要方法之一,但利用其中第二个重要极限求其他较复杂的1∞型未定式极限过程相当繁琐,初学者很难掌握.本文给出了一种求这类极限的简便方法,不但行之有效,而且方便易学,相信会对求这类极限起到事半功倍的作用.

1^∞型极限的探讨

运用α=O(β) ,α=o(β) ,β =o(α)在 1∞ 型极限中的理论和α～ β的代换在 1∞ 型极限中的应用 ,论述了 1∞ 型极限的解题方法 ,克服了教科书中解题方法单一的缺点 ,拓宽了求解此类型极限的思路。

未定式1~∞型极限的计算

本文通过论证和举例给出所有未定式1∞型极限利用重要极限limx→∞(1+1/x)x=e计算的可行性,且方法简捷、有效。

1~∞型极限的又一种求法

本文通过若干例题说明了1∞型极限的又一种求法,得出了1∞型极限求法的一些具体法则。

一种有效公式法求解1~∞型的极限

1~∞型的极限属于不确定型的极限,原有的基本方法是通过将其转化为确定型,然后利用重要极限的推广形式进行求解,过程略显繁琐与复杂。本文通过结合等价无穷小,提出了一种有效公式法来求解1~∞型的极限,使求解过程变得简单、快捷。

1~∞型极限源于重要极限lim x→0(1+x)^(1/x),又胜于重要极限

举例说明1∞型极限比重要极限limx→0 (1+x)^(1/x)

巧解1^∞型极限

本文充分利用等价无穷小量的代换,归纳出1∞未定型极限的几种巧妙方法,与《高等数学》教材中的常用方法相比。

等价替换在1~∞型极限中的应用

在满足一定的条件下,1~∞型极限可以使用等价替换,转换为第二个重要极限。该方法与以多项式为主项的等价替换、基本等价关系式和带有佩亚诺型余项的泰勒展开式相结合,可快速求解许多1~∞型极限。

浅谈两个重要极限的应用型教学

两个重要极限在高等数学中占着非常重要的位置,不仅是函数求极限的一种方法,而且它的应用思想——凑形式,在以后的教学中将会被广泛应用。本文主要讲述这两个重要极限的推广型与应用性,对于第一个极限的应用(0/0型)在凑形式时要保证变量的一致性和变量趋于零,对于第二个极限的应用(1~∞型)在凑形式时要抓两点:"1+"和"互倒"。

Research on 1-3 Orthogonal Anisotropic Piezoelectric Composite Material Sensors-

Piezoelectric composite material (PCM) is an important branch of modernsensor and actuator materials with wide applications in smart structures. In this paper, based onpiezoelectric ceramic, composite and experimental mechanics theories, a kind of 1-3 orthogonalanisotropic PCM (OAPCM) sensor is developed, and the sensing principle is analyzed to describesensor behaviors. In order to determine strain and stress on isotropic or orthogonal anisotropiccomponent surface, the relationships between strain and stress are established. The experimentalresearch on 1-3 OAPCM sensor is carried out in uniaxial and biaxial stress states. The results showthat 1-3 OAPCM sensors offer orthotropic properties of piezoelectricity, and sensing equations canbe used for strain or stress measurement with good accuracy.

Is Glucagon-like peptide-1, an agent treating diabetes, a new hope for Alzheimer's disease?

Glucagon-like peptide- 1 （GLP- 1） has been endorsed as a promising and attractive agent in the treatment of type 2 diabetes mellitus （T2DM）. Both Alzheimer＇s disease （AD） and T2DM share some common pathophysiologic hallmarks, such as amyloid β （Aβ）, phosphoralation of tau protein, and glycogen synthase kinase-3. GLP-1 possesses neurotropic properties and can reduce amyloid protein levels in the brain. Based on extensive studies during the past decades, the understanding on AD leads us to believe that the primary targets in AD are the Aβ and tau protein. Combine these findings, GLP- 1 is probably a promising agent in the therapy of AD. This review was focused on the biochemistry and physiology of GLP- 1, communities between T2DM and AD, new progresses of GLP - 1 in treating T2MD and improving some pathologic hanmarks of AD.

Transplantation for the treatment of type 1 diabetes

Transplantation of pancreatic tissue, as either the intact whole pancreas or isolated pancreatic islets has become a clinical option to be considered in the treatment of patients with type 1 insulin-dependant diabetes mellitus. A successful whole pancreas or islet transplant offers the advantages of attaining normal or near normal blood glucose control and normal hemoglobin Alc levels without the risks of severe hypoglycemia associate with intensive insulin therapy. Both forms of transplants are also effective at eliminating the occurrence of significant hypoglycemic events （even with only partial islet function evident）. Whereas whole pancreas transplantation has also been shown to be very effective at maintaining a euglycemic state over a sustained period of time, thus providing an opportunity for a recipient to benefit from improvement of their blood glucose control, it is associated with a significant risk of surgical and post-operative complications. Islet transplantation is attractive as a less invasive alternative to whole pancreas transplant and offers the future promise of immunosuppression-free transplantation through pretransplant culture. Islet transplantation however, may not always achieve the sustained level of tight glucose control necessary for reducing the risk of secondary diabetic complications and exposes the patient to the adverse effects of immunosuppression. Although recent advances have led to an increased rate of obtaining insulin-independence following islet transplantation, further developments are needed to improve the longterm viability and function of the graft to maintain improved glucose control over time.

EXPRESSION OF mRNA FOR MEMBRANE-TYPE 1, 2, AND 3 MATRIX METALLOPROTEINASES IN HUMAN LARYNGEAL CANCER

To investigate correlation of expressions of membrane-type 1, 2, and 3 matrix metalloproteinases (MT1, MT2, and MT3-MMP) to the invasion and metastases in laryngeal cancer. Methods Reverse transcription-polymerase chain reaction (RT-PCR) was used to examine the mRNA level of MT1, MT2, and MT3-MMP in 24 patients with laryngeal cancer. The relationships of these three MT-MMP expressions to clinico-pathology were analyzed by statistics. Results The expressions of MT1, MT2, and MT3-MMP were significantly higher in laryngeal cancer tissues than those in para-tumorous tissues (P < 0.01) and had a close relationship with invasive depth (P < 0.05). But no significantly different expressions of these three MT-MMPs were found in different primary location and different histological grade of laryngeal cancer (P > 0.05). The expression of MT1-MMP was obviously higher in patients with metastatic lymph nodes than that in patients without metastatic lymph nodes (P < 0.05). Conclusion MT1, MT2, and MT3-MMP play an important role in the progression of laryngeal cancer, and MT1-MMP may serve as a reliable marker in estimating invasive and metastatic potency of laryngeal cancer. Suppressing expressions of MT1, MT2, and MT3-MMP early may inhibit the invasion and metastases of laryngeal cancer.

Expression of interferon inducible protein-10 in pancreas of mice

AIM: To investigate the expression of interferon inducible protein-10 (IP-10) in pancreas of mice and to discuss its possible role in the pathogenesis of type 1 diabetes.METHODS: Non-obese diabetic (NOD) mice were used as experiment group and BALB/c mice as non-diabetic prone model. Immunohistochemistry method was used to evaluate the expression of IP-10 in the pancreas of NOD mice and BALB/c mice. Immunoelectron microscope was used to show the location of IP-10 in pancreatic islet β cells.RESULTS: Pancreatic islets were positively stained in all the NOD mice. Insulitis could be found in mice at the age of 4 wk. The weakly positive results were found in control group with no insulitis. Immunoelectron microscopy further demonstrated that IP-10 was produced by pancreatic β cells and stored in cytoplasm of the cells.CONCLUSION: IP-10 can be largely produced in pancreatic islets of NOD mice at the age of 2 wk when there is no significant insulitis, and may play an important part in the pathogenesis of type 1 diabetes by attracting immune cells to infiltrate the pancreatic islets.

Gene therapy for type 1 diabetes mellitus in rats by gastrointestinal administration of chitosan nanoparticles containing human insulin gene

AIM:To study the expression of human insulin gene in gastrointestinal tracts of diabetic rats. METHODS: pCMV.Ins, an expression plasmid of the human insulin gene, wrapped with chitosan nanoparticles, was transfected to the diabetic rats through lavage and coloclysis, respectively. Fasting blood glucose and plasma insulin levels were measured for 7 d. Reverse transcription polymerase chain reaction (RT-PCR) analysis and Western blot analysis were performed to confirm the expression of human insulin gene. RESULTS: Compared with the control group, the fasting blood glucose levels in the lavage and coloclysis groups were decreased significantly in 4 d (5.63 ± 0.48 mmol/L and 5.07 ± 0.37 mmol/L vs 22.12 ± 1.31 mmol/L, respectively, P < 0.01), while the plasma insulin levels were much higher (32.26 ± 1.81 μIU/mL and 32.79 ± 1.84 μIU/mL vs 14.23 ± 1.38 μIU/mL, respectively, P < 0.01). The human insulin gene mRNA and human insulin were only detected in the lavage and coloclysis groups. CONCLUSION: Human insulin gene wrapped with chitosan nanoparticles can be successfully transfected to rats through gastrointestinal tract, indicating that chitosan is a promising non-viral vector.

Utility of an upright-type 11-gauge stereotactic vacuum-assisted biopsy device (Mammotome) for the diagnosis of breast microcalcifications

Objective: The aim of this study was to evaluate the utility of an upright-type 11-gauge stereotactic vacuumassisted biopsy device (Mammotome) for the diagnosis of breast microcalcifications Methods: Between May 2001 and October 2005, 154 biopsies in 152 patients with microcalcifications were performed using the upright-type 11-gauge stereotactic vacuum-assisted biopsy device. Patients in whom this biopsy was diagnosed as carcinoma or a borderline lesion, had a subsequent surgical excision of the lesion. Histopathological and radiological features of the two specimens were then compared with each other. Results: Microcalcification was identified on specimen mammograms and microscopic slides in 97.4% of cases. Of 154 Mammotome biopsies 98 (63.6%) were benign, 51 (33.1%) were malignant, 3 (1.9%) showed atypical hyperplasia, and 2 (1.3%) were indeterminate, respectively. Of the 48 cases that received surgical excision, 6 of 36 ductal carcinomas in situ (16.7%) upstaged to invasive ductal carcinoma and 1 of 2 atypical ductal hyperplasias was upstaged to ductal carcinoma in situ. The positive predictive value of the 11-gauge Mammotome for the diagnosis of invasion in breast cancer was 100%. Linear calcification and pleomorphic calcification linear/segmental distribution was reliable indications of malignancy. The mean follow-up time of the benign lesions was 22 months, and without evidence of lesion growth. Complications included vasovagal reactions (6.3%), bleeding (0.6%) and hematoma (2.6%). Conclusion: The upright stereotactic 11-gauge Mammotome procedure is an effective and reliable method for the diagnosis of breast microcalcifications. It has minimal side effects. For lesions diagnosed as ADH or DCIS with the 11-gauge Mammotome, subsequent surgical excision should be performed.

关于0^0,∞^0及1^∞不定式的几个定理

在求两个无穷小（无穷大）的积或商的极限过程中，常常把其中的无穷小（无穷大）用与其等价的无穷小（无穷大）来替换。本文证明了这一方法对于０＾－型、∞＾０型以及１＾∞型不定式也是成立的。此外，本文还给出了两类常见的０＾０型不定式的值。

An Exactly Solvable Spin-1 Model under External Magnetic Field

A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume-Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m and square magnetic moment q are investigated as functions of temperature and external magnetic fieId both for ferromagnetic and antiferromagnetic couplings. In the study, we propose a possible mechanism of the plateau based on the exchange couplings.

Low Frequencies of CCR5-Δ32 and CCR5-m303,but High Frequencies of CCR2-641 and SDF1-3'A Alleles in Indigenous Ethnic Groups in China's Mainland

Objective: The aim in this study was to identify the allelicfrequencies of the chemokine (SDF1-3'A) and chemokinereceptor (CCR5△32, CCR5m303 and CCR2-64I) genesresistant to HIV-1 infection and/or disease progression inindigenous Chinese populations. Methods: By using QIAamp DNA Blood Mini Kit, thegenomic DNA samples were purified from whole peripheralblood of healthy individuals (n=2067) from Han, Uygur,Mongolian and Tibetan ethnic groups, as well as Han patientsincluding HIV-1 carriers (n=330), patients with other sexuallytransmitted diseases (STDs, n=259) and intravenous drugusers (IVDUs, n=125). The allelic polymorphisms wereidentified by means of PCR or PCR-RFLP analyses. Thesequences of randomly selected amplified PCR products werefurther confirmed by direct DNA sequencing. Results: The mutant frequencies were identified to be0%～3.48% for CCR5△32, 0% for CCR5m303,19.15%～28.79% for CCR2-64 and 19.10%～28.73% for SDF1-3'A alleles, respectively, in Chinese healthy individuals fromfour ethnic groups. Our findings indicated the allelicfrequencies vary among the different ethnic groups.Furthermore, the HIV-1 carriers, STD cases and IVDUs (all ofHan ethnicity) were found to have the allelic frequencies of0%～0.19% (CCR5△32), 0% (CCR5m303), 19.31%～20.45%(CCR2-64) and 25.61%～26.83% (SDF1-3'A) with minorvariations in their frequencies between the patients andhealthy Han groups. There was no CCR5-m303 mutationfound in any subject in this study. Conclusion: The examined subjects of four Chinese ethnicorigins showed lower frequencies of CCR5△32 andCCR5m303 alleles, but higher frequencies of mutant CCR2-64I and SDF1-3'A alleles compared to those identified innorthern-European and American Caucasians. Thesignificance of the different frequencies and polymorphisms ofthe above alleles in Chinese populations needs to be furtherexamined in HIV-1/AIDS diseases.