Abstract:
Background: CD133 could be characterized as a “stem-like” cell subpopulation and an invasive tumor phenotype. The objectives of this study were to investigate the relationship of CD133 and other remodeling factors such as matrix metalloproteinases (MMP) in the brain tumors. Methods: Tumors from 13 patients with brain tumors (8 lung cancer metastasis, 3 breast cancer metastasis, 2 gliomas) were studied to investigate the expression-patterns of CD133, EGFR, MT1-MMP, and MMP7 using the immunostaining and RT-PCR analysis. Results: EGFR immunostaining was detected in 75% (6/8) and 67% (1/3) of brain metastasis from lung adenocarcinoma and breast cancer, respectively. MT1-MMP immunostaining was also detected in 73% (8/11) of these brain metastasis. CD133 was not detected in these 13 patients. EGFR immunostaining was detected in 75% (6/8) and 67% (1/3) of brain metastasis from lung adenocarcinoma and breast cancer, respectively. MT1-MMP immunostaining was also detected in 73% (8/11) of these brain metastasis. CD133 was not detected in these 13 patients. Conclusions: The expression of CD133 indicates a marker for brain tumor initiating.

Abstract:
We have developed a hybrid hydrogel that is formed from a crosslinkable polymeric micelle and a
polyamine. Under optimal conditions, the hydrogel rapidly formed in one second after a crosslinkable
polymeric micelle solution was mixed with a polyamine solution. We could change the
hydrogel’s gelation properties, such as the storage modulus and gelation time by tuning the molecular
weights of block copolymers and by tuning the pH of the dissolving-solvent of the hydrogel’s
constituent components. Furthermore, we have clarified here that the structural difference among
the micelles acting as crosslinkers can affect the gelation properties of the hydrogel. According to
our findings, the hydrogel that was formed from the polymeric micelles possessing a highly
packed (i.e., well-entangled or crosslinked) inner core exhibited a higher storage modulus than
the hydrogel that was formed from the polymeric micelles possessing a lowly packed structure.
Our results demonstrate that a microscopic structural difference among crosslinkers can induce a
macroscopic change in the properties of the resulting hydrogels. For medical applications, the hydrogel
proposed in the present paper can encapsulate the hydrophobic compounds in crosslinkers
(polymeric micelles) so that the hydrogel can be available as the biomaterial for their sustained
release.

Abstract:
Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise v_{c}(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k); 2) the observation matrix H; 3) the variance of the state vector x(k); 4) the system matrix for the colored observation noise v_{c}(k); 5) the variance of the colored observation noise; 6) the input noise variance in the state equation for the colored observation noise.

Abstract:
We calculate in a numerically friendly way the Fourier transform of a non-integrable function, such as , by replacing F with R^{-1}FR, where R represents the resolvent for harmonic oscillator Hamiltonian. As contrasted with the non-analyticity of at in the case of a simple replacement of F by , where and represent the momentum and position operators, respectively, the turns out to be an entire function. In calculating the resolvent kernel, the sampling theorem is of great use. The resolvent based Fourier transform can be made supersymmetric (SUSY), which not only makes manifest the usefulness of the even-odd decomposition ofin a more natural way, but also leads to a natural definition of SUSY Fourier transform through the commutativity with the SUSY resolvent.

Abstract:
Peltier current lead was proposed to reduce heat leak from the current lead. The temperature of the hot side of semiconductors was kept to be room temperature and the liquid nitrogen was used to cool the system in the experiment. The experiment confirmed the principle of the Peltier current lead, and the reduction of the heat leak is calculated to be 30 % for the liquid helium system and 40 % for the liquid nitrogen system. We also proposed a new current lead system which is composed of semiconductors and high temperature superconducting material (HTS). This idea bases on the functionally gradient material (FGM), and the HTS is connected to the semiconductor directly. The temperature of the hot side of semiconductor is kept to be the liquid nitrogen temperature, the temperature of HTS can be expected to be lower than 77 K. Therefore, we can expect high current capacity of the HTS and/or high stability of the HTS. We use BiSb as a N-type semiconductor and BiTe as a P-type semiconductor in the experiment, and the temperature of the cold side of the semiconductor is 73 K in this experiment.

Abstract:
Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is colored. This paper, from the viewpoint of the innovation theory, based on the recursive least-squares (RLS) Wiener fixed-point smoother and filter for the colored observation noise, newly proposes the RLS Wiener fixed-interval smoothing algorithm in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise (v_c)(k). The RLS Wiener fixed-interval smoother uses the following information: (a) the system matrix for the state vector x(k); (b) the observation matrix H; (c) the variance of the state vector; (d) the system matrix for the colored observation noise (v_c)(k); (e) the variance of the colored observation noise; (f) the input noise variance in the state equation for the colored observation noise.

Abstract:
In 1969 Mocanu [1] introduced and studied a new class of analytic functions consisting of ±-convex functions. Many mathematicians have studied and shown the properties of this class. Now we will define new classes like that Mocanu class and then investigate and give some results. The class of ±-convex functions of order 2 partially includes Mocanu's class.

Abstract:
Low-temperature heat capacity of potassium germanate glasses (xK2O?(100-x)GeO2; x=0.0, 10.1, 19.0, 28.2, 39.0) (x indicates K2O mol% content) has been measured in the temperature range from 2 to 50 K with K2O content. From a result of the heat capacity Cp, it has been found that an excess heat capacity is not caused by a regular thermal motion but an interaction. In addition, it has also been found that a relationship between a maximum of reduced excess heat capacity CpT -3max and elastic modulus is dual. Moreover, a ‘hole’ model of liquid theory was applied to explain the formation of resonant mechanism. This model leads us to an idea that the excess heat capacity is described by degree of freedom of reallocated-and-isolated-structural units. Consequently, we conclude that the excess heat capacity is caused by the reallocated-main-network structure containing holes resonant with the reallocated-and-isolated-microstructural units.

Abstract:
Retroperitoneal lipoma presenting with a nutcracker-like phenomenon is extremely rare. I experienced a case of a 65-year-old man presenting with left flank pain and macrohematuria intermittently for 3 years. Computed tomography revealed a lipoma at the left pedicle of the kidney, 30？mm in diameter, causing a curving of the left renal artery and dilatation of the left renal vein. This patient was treated successfully by retroperitoneoscopic resection of the lipoma. There have been no symptoms for 10 years after the operation. 1. Introduction The nutcracker syndrome was first reported in 1972 by Schepper [1]. Compression of the left renal vein between the superior mesenteric artery and aorta can cause venous hypertension and formation of ureteral and renal pelvic venous varicosities. Related symptoms and hematuria have been described as the nutcracker syndrome previously [1, 2], but it remains unclear why compression of the left renal vein by the superior mesenteric artery afflicts only a few patients and which anatomical details are related to the pathophysiological mechanism. Actually, there are many other causes of compression of the left renal vein such as aneurysm, curving of the left renal artery, or renal arterial and venous anomalies [3–6]. I herein report a case with retroperitoneal lipoma presenting with a nutcracker-like phenomenon. 2. Case Report A 65-year-old man has been presenting with intermittent gross hematuria and left flank pain for 3 years. There was no history of renal trauma, urinary tuberculosis, urinary bilharziasis, or other diseases. Physical examination revealed no abnormal findings. Laboratory test results were within normal ranges except for microscopic hematuria. Ultrasonography of the urinary tract and excretory urography were normal. Computerized tomography confirmed retroperitoneal lipoma around the left renal pedicle, 30 mm in diameter, causing a curving of the left renal artery and dilatation of the left renal vein (Figure 1). His condition was diagnosed as retroperitoneal lipoma that caused abnormal renal arterial traveling and compression of the renal vein. On June 25, 2003, retroperitoneoscopic lipoma resection was performed with the standard 3-port technique. Grossly, lipoma is a yellow lobulated and encapsulated mass (Figure 2); histopathologically, it consists entirely of mature fat (Figure 3). Figure 1: CT scan reveals retroperitoneal lipoma around the left renal pedicle, 30 mm in diameter, causing a curving of the left renal artery and dilatation of the left renal vein. Figure 2: Retroperitoneal lipoma is a

Abstract:
The notion of a virtual knot introduced by L. Kauffman induces the notion of a virtual braid. It is closely related with a welded braid of R. Fenn, R. Rimanyi and C. Rourke. Alexander's and Markov's theorems for virtual knots and braids are proved. Similar results for welded knots and braids are also proved.