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Under the assumption that the initial data belong to suitable Sobolev spaces, we derive the better decay estimate of the second order derivatives for the initial boundary value problem for degenerate dissipative wave equations of Kirchhoff type.

Consider the initial boundary value problem for degenerate dissipative wave equations of Kirchhoff type. When the wave coefficient ρ > 0 or the initial energy E(0) is small, we show the global existence theorem.

Consider the Cauchy problem for the non-degenerate Kirchhoff type dissipative wave equations with the initial data belonging to (H2(RN)∩L1(RN))×(H1(RN)∩L1(RN)). Using the Fourier transform method in the L2 ∩ L1-frame, we can improve the decay rates of the energies given by the energy method of the L2-frame.

A K+-promoted Diels–Alder reaction of 1,4,9,10-anthradiquinone with various dienes is achieved in the presence of a self-assembled macrocyclic boronic ester., A K+-promoted Diels–Alder reaction of 1,4,9,10-anthradiquinone with various dienes is achieved in the presence of a self-assembled macrocyclic boronic ester [2+2]crown containing two crown ether moieties. The reaction rate is remarkably accelerated (up to 206-fold) compared to that in the absence of the promoter. Furthermore, the reaction proceeds regioselectively to yield an internal adduct. The self-assembly protocol was also demonstrated.

We study on the Cauchy problem for non-degenerate Kirchhoff type dissipative wave equations ρu′′ + a (||A1/2u(t)||2) Au + u′ = 0 and (u(0), u′(0)) = (u0, u1), where u0 ≠ 0 and the nonlocal nonlinear term a(M) = 1+Mγ with γ > 0. Under the suitably smallness condition, we derive the upper decay estimates of the solution u(t) for the case of 0 < γ < 1 in addition to γ ≥ 1.

Background: During laparoscopic appendectomy, several methods and devices can be used to close the appendicular stump, such as endoloops, linear staplers, clips, and open purse-string sutures. The Double-shanked Titanium Ligation Clip® (DS clip; B. Braun Aesculap, Tuttlinger, Germany), a new device that can be used to close the appendicular stump, was approved for use in Japan in March 2015. We report a case of effective appendix stump closure using DS clips. Case presentation: An 81-year-old man was admitted to our hospital with complaints of severe pain in the right lower quadrant of the abdomen. Abdominal contrast-enhanced computed tomography showed a thickened appendix (1.7 cm in diameter) with fecal stones, while acute inflammatory signs were visible around the appendix. He was diagnosed with acute appendicitis for which laparoscopic appendectomy was performed with a curative intent. It was difficult to mobilize the cecum because of inflammation, so we attempted to use DS clips instead of linear staplers. A histological examination revealed gangrenous appendicitis. The patient’s postoperative course was uneventful and he was discharged 10 days postoperatively. We also used DS clips to close the appendicular stump in 12 other cases. We observed no intra- or postoperative complications and no cases of mortality. Conclusion: The management of an appendicular stump using DS clips during laparoscopic appendectomy was simple, safe, and cost-effective. DS clips may be an alternative method to linear staplers.