ON THE CENTRAL LIMIT THEOREM IN PRODUCT SPACES

Suppose that E and F are separable Banach spaces, X and Y are independent symmetric E and F-valued random vectors respectively. This paper is devoted to the study of the central limit theorem for X Y in the injective and projective tensor product spaces E F and E F. Special attention is paid to l2 l2. In addition, two counter-examples are given.

An in vivo study of the biodistribution of gold nanoparticles after intervaginal space injection in the tarsal tunnel

The biodistribution of gold nanoparticles （AuNPs） is closely related to toxicological effects and is of great concern because of their potential application in diverse biomedical areas. However, with the discovery of novel anatomic and histological structures for fluid transport, the underlying mechanisms involved in the in vivo transport and biodistribution of AuNPs require further in-depth investigations. In the current study, we investigated the biodistribution of 10-nm AuNPs in rats after intervaginal space injection （ISI） in the tarsal tunnel, where a focal point of tendons, vessels, and nerve fibers may optimally connect to other remote connective tissues. The intravenous injection （IVI） of AuNPs served as a control. The blood and organs were collected at 5, 15, and 30 min and at 1, 4, 12, and 24 h after injection for quantitative analysis of Au distribution with inductively coupled plasma mass spectrometry （ICP-MS）. IVI and ISI yielded significantly different results： The AuNP content in the blood after ISI was much lower than that after IVI; was similar in the lungs, heart, and intestines; and was higher in the skin and muscle. These findings were supported by the ratios of AuNP content and relative organ AuNP distribution proportions. Our results demonstrated a fast, direct, and the circulation-independent AuNP-organ transport pathway, which may improve our understanding of physiological and pathological biodistribution processes in biological systems. Furthermore, these results provide novel insights into the in vivo transport and biodistribution of AuNPs, which may lead to novel and efficient therapeutic and administration strategies.

Flow behavior of liquid metal in the connected fascial space： Intervaginal space injection in the rat wrist and mice with tumor

The fascia and the fascial space can help provide a better understanding of the body. An intervaginal space injection （ISI） provides unique advantages that require further investigation. An upper limb model including physiological conditions and the tumor process was chosen to determine the flow behavior of liquid metal after ISI. In normal rats, after the injection of liquid metal into the intervaginal space comprising tendons, vessels, and nerves, magnetic resonance imaging and an anatomy experiment indicated that the liquid metal wrapped around the fascial space and finally reached the fingertip downstream and the armpit upstream in addition to the neurovascular bundle without vessels or lymph nodes. Using environmental scanning electron microscopy （ESEM） images, we discovered that the liquid metal was wrapped around the fibers of the fascia and moved forward in microscale or nanoscale areas. These data confirmed a fascia-based pathway. In tumors, the liquid metal moved to the tumor capsule through the damaged spot, where cancer cells destroy the integrity of the fascia between the normal cells and cancer cells. The liquid metal partly wrapped around the tumor and separated the tumor from the surrounding normal muscle. The ESEM images showed that fibers of the fascia penetrated the tumor, thus forming a network through which the liquid metal penetrated the tumor. Our study illustrated the physiological and pathological flow behavior of liquid metal in the upper limb after ISI and demonstrated a nonvascular pathway in the fascia. ISI may be useful for clinical treatment in the fascial pathway.

Thoracic interstitial injection of drug-liposomes in mice for treating atherosclerosis

Intervaginal space injection(ISI)is a novel mode of administration investigated over the last decade.After injecting nanoparticles into the intervaginal space,they can be transported along low flow resistance channels into the interstitial space.This transport has a certain delivery direction,and site-specific injection can work on specific organs or tissues.In this study,the thorax,a new ISI site in the interstitial surrounding the internal thoracic artery named the thoracic interstitial injection(tISI)was investigated.To prove the targeting ability of the tISI,two sizes of gold nanoparticles(AuNPs)(47 and 87 nm)were administered to mice.After 1 h,the biodistribution of AuNPs in the tissues was measured via single particle inductively coupled plasma mass spectrometry(spICP-MS).The results showed that the concentration of AuNPs in the aorta after tISI injection was significantly higher than that after intravenous injection.Moreover,fewer nanoparticles with larger particle sizes were observed to have entered the blood and were better targeted to the aorta.Thereafter,tanshinone IIa sodium sulfonate liposomes were administered for the treatment of aortic atherosclerosis.The proportion of aortic plaques in atherosclerotic Apoe-/-mice administered via tISI was significantly lower than that in other model animals(P<0.001).Furthermore,the proteoglycan content and CD68-positive cell count in the plaques were significantly reduced.The vascular elastic fibers at the plaque site were thickened,and fractures were reduced.tISI was,therefore,determined to be an effective strategy for the treatment of atherosclerotic aortic plaques.

On Universally Left-stability of ε-Isometry

Let X, Y be two real Banach spaces and ε≥0. A map f ： X → Y is said to be a standard ε-isometry if│││f/（x） - f（y）││ - ]ix - Y││x-y││ ε for all x,y C X and with f（O） = O. We say that a pair of Banach spaces （X, Y） is stable if there exists γ〉 0 such that, for every such ε and every standard v-isometry f ： X → Y, there is a bounded linear operator T ： L（f） → f（X） → X so that ││Tf（x） - x││ ≤γε for all x E X. X（Y） is said to be universally left-stable if （X, Y） is always stable for every Y（X）. In this paper, we show that if a dual Banach space X is universally left-stable, then it is isometric to a complemented w＊-closed subspace of ∞ （1） for some set F, hence, an injective space; and that a Banach space is universally left-stable if and only if it is a cardinality injective space; and universally left-stability spaces are invariant.

Production of Transgenic Korean Native Cattle Expressing Enhanced Green Fluorescent Protein Using a FIV-Based Lentiviral Vector Injected into MII Oocytes

The potential benefits of generating and using transgenic cattle range from improvements in agriculture to the production of large quantities of pharmaceutically relevant proteins. Previous studies have attempted to produce transgenic cattle and other livestock by pronuclear injection and somatic cell nuclear transfer, but these approaches have been largely ineffective; however, a third approach, lentivirus-mediated transgenesis, has successfully produced transgenic livestock. In this study, we generated transgenic （TG） Korean native cattle using perivitelline space injection of viral vectors, which expressed enhanced green fluorescent protein （EGFP） systemically. Two different types of lentiviral vectors derived from feline immunodeficiency virus （FIV） and human immunodeficiency virus （HIV） carrying EGFP were injected into the perivitelline space of MII oocytes. EGFP expression at 8-cell stage was significantly higher in the FIV group compared to the HIV group （47.5% ± 2.2% v.s. 22.9% 4± 2.9%）. Eight-cell embryos that expressed EGFP were cultured into blastocysts and then transferred into 40 heifers. Ten heifers were successfully impregnated and delivered 10 healthy calves. All of these calves expressed EGFP as detected by in vivo imaging, PCR and Southern blotting. In addition, we established an EGFP-expressing cell line from TG calves, which was followed by nuclear transfer （NT）. Recloned 8-cell embryos also expressed EGFP, and there were no differences in the rates of fusion, cleavage and development between cells derived from TG and non-TG calves, which were subsequently used for NT. These results illustrate that FIV-based lentiviruses are useful for the production of TG cattle. Moreover, our established EGFP cell line can be used for additional studies that involve induced pluripotent stem cells.