Disclosed herein is a method for selectively reducing, using electrical energy, CO.sub.2 to carbon monoxide or formic acid, a catalyst for use in the method, and an electrochemical reduction system. The method for producing carbon monoxide or formic acid by electrochemically reducing carbon dioxide of the present invention includes (a) reacting carbon dioxide with a metal complex represented by formula (1), and (b) applying a voltage to a reaction product of the carbon dioxide and the metal complex represented by formula (1):

##STR00001##

Disclosed herein is a method for selectively reducing, using electrical energy, CO.sub.2 to carbon monoxide or formic acid, a catalyst for use in the method, and an electrochemical reduction system. The method for producing carbon monoxide or formic acid by electrochemically reducing carbon dioxide of the present invention includes (a) reacting carbon dioxide with a metal complex represented by formula (1), and (b) applying a voltage to a reaction product of the carbon dioxide and the metal complex represented by formula (1):

##STR00001##

Described herein are methods of using compounds of Formula (I) to modulate PKM2 activity in a subject. These compounds are represented by Formula (I): wherein R.sup.1, R.sup.2, L.sup.1, and L.sup.2 are as defined herein.

##STR00001##

Described herein are compounds that activate pyruvate kinase, pharmaceutical compositions and methods of use thereof. These compounds are represented by Formula (I) wherein R.sup.1, R.sup.2, R.sup.a, R.sup.b, R.sup.j, R.sup.k, and Q are as defined herein

##STR00001##

Described herein are compounds that activate pyruvate kinase, pharmaceutical compositions and methods of use thereof. These compounds are represented by Formula (I) wherein R.sup.1, R.sup.2, R.sup.a, R.sup.b, R.sup.j, R.sup.k, and Q are as defined herein

##STR00001##

Described herein are methods of using compounds of Formula (I) to modulate PKM2 activity in a subject. These compounds are represented by Formula (I): ##STR00001##
wherein R.sup.1, R.sup.2, L.sup.1, and L.sup.2 are as defined herein.

Described herein are methods of using compounds of Formula (I) to modulate PKM2 activity in a subject. These compounds are represented by Formula (I): ##STR00001##
wherein R.sup.1, R.sup.2, L.sup.1, and L.sup.2 are as defined herein.

A heterocyclic compound represented by the general formula (1) or a salt thereof: ##STR00001## wherein m, l, and n respectively represent an integer of 1 or 2; X represents O or CH.sub.2; R.sup.1 represents hydrogen, a lower alkyl group, a hydroxy-lower alkyl group, a protecting group, or a tri-lower alkylsilyloxy-lower alkyl group; R.sup.2 and R.sup.3, which are the same or different, each independently represent hydrogen or a lower alkyl group; or R.sub.2 and R.sub.3 are bonded to form a cyclo-C3-C8 alkyl group; and R.sup.4 represents an aromatic group or a heterocyclic group, wherein the aromatic or heterocyclic group may have one or more arbitrary substituent(s).

This method for producing a fullerene derivative is a method for producing a fullerene derivative having a partial structure shown by formula (1) by reacting a predetermined halogenated compound and two carbon atoms adjacent to each other for forming a fullerene skeleton in a mixed solvent of an aromatic solvent and an aprotic polar solvent having a CO or SO bond in the presence of at least one metal selected from the group comprising manganese, iron, and zinc;

##STR00001##

(in formula (1), C* are each carbon atoms adjacent to each other for forming a fullerene skeleton, A is a linking group having 1-4 carbon atoms for forming a ring structure with two C*, in which a portion thereof may be a substituted or condensed group).

This method for producing a fullerene derivative is a method for producing a fullerene derivative having a partial structure shown by formula (1) by reacting a predetermined halogenated compound and two carbon atoms adjacent to each other for forming a fullerene skeleton in a mixed solvent of an aromatic solvent and an aprotic polar solvent having a CO or SO bond in the presence of at least one metal selected from the group comprising manganese, iron, and zinc;

##STR00001##

(in formula (1), C* are each carbon atoms adjacent to each other for forming a fullerene skeleton, A is a linking group having 1-4 carbon atoms for forming a ring structure with two C*, in which a portion thereof may be a substituted or condensed group).