On the nullstellensätze for stein spaces and C-analytic sets.

In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).

Djabote [videorecording]: Senegalese drumming & song from master drummer Doudou N'Diaye Rose

A film of Eric Serra's audio recording session of Doudou N'Diaye Rose and his drumming ensemble outdoors on the island of Gorée, off the coast of Dakar, Senegal. The film concentrates on two performances -- one shot in daytime, and one at night. Two performances are filmed, punctuated by images of the island.

Charles M. Alexander : a romance of song and soul-winning /

Mode of access: Internet.

Karen Stein

Scene showing a group of men, women, and children. The men appear to be members of the Grand Army of the Republic, possibly the Gov. Crapo Post #145

Gems of German song (revised edition) for low voice.

English and German words with piano accompaniment.

Prayer and song-book in honor of good mother St. Anne : to be used at St. Augustine's R.C. Church during the annual double novena before the Most Precious Relic Shrine from July 18th to July 26th, the feast of St. Anne.

Cover title.

Spanish America in song and story, selections representing Hispano-American letters from the conquest to the present day,

Mode of access: Internet.

The fountain of sacred song : a collection of new church music, for choirs, congregations, singing schools and conventions /

Publisher's advertisements: back cover.

White and Negro spirituals, their life span and kinship, tracing 200 years of untrammeled song making and singing among our country folk, with 116 songs as sung by both races.

"The tune comparative list. One hundred and sixteen melodies of white people paired with same number of Negro-sung variants": p. [145]-227.

Kaleidophone : new resources of melody and harmony : pitch scales in relation to chord structures : an aid to composers, performers, arrangers, teachers, song-writers, students, conductors, critics, and all who work with music /

Mode of access: Internet.

Lied der Walküre (The song of the Valkyr) ... Für eine höhere Singstimme mit Begleitung des Orchesters. Op. 36, Nr. 4. Partitur.

Pl. no.: Part.B.1834.

Song without words, Op. 56 [music].

Mode of access: Internet.