Abstract: In an arithmetic operation system, an evaluation unit calculates a difference amount between a teaching signal and an estimated signal. The teaching signal is a spatial distribution signal observed with respect to a spatial structure on a path of an emission wave in a target space (i.e., a teaching space) by using the emission wave. In addition, the estimated signal is a signal for comparing with the teaching signal, and is an estimated spatial distribution signal. The estimated signal is formed based on estimated density associated to each sample point acquired from a spatial estimation model, by a sampling unit inputting information about a position of each of a plurality of sample points on the path to the spatial estimation model. An updating unit updates the spatial estimation model, based on the difference amount.

Abstract: A composition includes: a compound including an aromatic ring; and a first polymer including a first structural unit represented by formula (1) and a second structural unit represented by formula (2). A content of the first polymer with respect to 100 parts by mass of the compound is no less than 0.1 parts by mass and no greater than 200 parts by mass. R1 represents a hydrogen atom or a substituted or unsubstituted monovalent hydrocarbon group; and R2 represents a substituted or unsubstituted monovalent hydrocarbon group. R3 represents a hydrogen atom or a substituted or unsubstituted monovalent hydrocarbon group; L represents a single bond or a divalent linking group; Ar represents a group obtained by removing (n+1) hydrogen atoms from a substituted or unsubstituted aromatic ring; R4 represents a hydroxy group or a monovalent hydroxyalkyl group; and n is an integer of 1 to 8.

Abstract: A composition includes: a compound including an aromatic hydrocarbon ring structure, and a partial structure represented by formula (1) which bonds to the aromatic hydrocarbon ring structure; and a solvent. The aromatic hydrocarbon ring structure has no fewer than 25 carbon atoms. In the formula (1), X represents a group represented by formula (i), (ii), (iii), or (iv); and *'s denote binding sites to two adjacent carbon atoms constituting the aromatic hydrocarbon ring structure. A method of producing a patterned substrate, includes applying the composition directly or indirectly on a substrate to form a resist underlayer film; forming a resist pattern directly or indirectly on the resist underlayer film; and carrying out etching using the resist pattern as a mask.

Abstract: A composition for resist underlayer film formation, includes a first compound and a solvent. The first compound includes a first group represented by formula (1) and a partial structure comprising an aromatic ring. In the formula (1), R1 represents a single bond or an oxygen atom, R2 represents a divalent chain or alicyclic hydrocarbon group having 1 to 30 carbon atoms, and * denotes a bonding site to a moiety other than the first group of the first compound.

Abstract: A composition for resist underlayer film formation contains: a compound having a partial structure represented by the following formula (1); and a solvent. In the formula (1): X represents a group represented by formula (i), (ii), (iii) or (iv). In the formula (i): R1 and R2 each independently represent a hydrogen atom, a substituted or unsubstituted monovalent aliphatic hydrocarbon group having 1 to 20 carbon atoms, or a substituted or unsubstituted aralkyl group having 7 to 20 carbon atoms provided that at least one of R1 and R2 represents the substituted or unsubstituted monovalent aliphatic hydrocarbon group having 1 to 20 carbon atoms or the substituted or unsubstituted aralkyl group having 7 to 20 carbon atoms; or R1 and R2 taken together represent a part of a ring structure having 3 to 20 ring atoms together with the carbon atom to which R1 and R2 bond.

Abstract: A composition for resist underlayer film formation contains a compound having a group represented by formula (1), and a solvent. R1 represents an organic group having 2 to 10 carbon atoms and having a valency of (m+n), wherein the carbon atoms include two carbon atoms that are adjacent to each other, with a hydroxy group or an alkoxy group bonding to one of the two carbon atoms, and with a hydrogen atom bonding to another of the two carbon atoms; L1 represents an ethynediyl group or a substituted or unsubstituted ethenediyl group; R2 represents a hydrogen atom or a monovalent organic group having 1 to 20 carbon atoms; n is an integer of 1 to 3; * denotes a bonding site to a moiety other than the group represented by the formula (1) in the compound; and m is an integer of 1 to 3.

Abstract: A composition contains: an aromatic ring-containing compound; a fluorine atom-containing polymer; and an organic solvent. The fluorine atom-containing polymer has: a first structural unit represented by formula (1); and a second structural unit represented by formula (2). In the formula (1), R1 represents a fluorine atom-containing monovalent organic group having 1 to 20 carbon atoms; and R2 represents a hydrogen atom or a monovalent hydrocarbon group having 1 to 20 carbon atoms. In the formula (2), R3 represents a monovalent hydrocarbon group having 1 to 20 carbon atoms; and R4 represents a hydrogen atom or a monovalent hydrocarbon group having 1 to 20 carbon atoms.

Abstract: The composition for film formation includes a compound including a group of the formula (1) and a solvent. In the formula (1), R1 to R4 each independently represent a hydrogen atom, a monovalent organic group having 1 to 20 carbon atoms, or R1 to R4 taken together represent a cyclic structure having 3 to 20 ring atoms together with the carbon atom or a carbon chain to which R1 to R4 bond. Ar1 represents a group obtained by removing (n+3) hydrogen atoms from an aromatic ring of an arene having 6 to 20 carbon atoms. n is an integer of 0 to 9. R5 represents a hydroxy group, a halogen atom, a nitro group, or a monovalent organic group having 1 to 20 carbon atoms.

Abstract: A composition for resist underlayer film formation contains: a compound having a partial structure represented by the following formula (1); and a solvent. In the formula (1): X represents a group represented by formula (i), (ii), (iii) or (iv). In the formula (i): R1 and R2 each independently represent a hydrogen atom, a substituted or unsubstituted monovalent aliphatic hydrocarbon group having 1 to 20 carbon atoms, or a substituted or unsubstituted aralkyl group having 7 to 20 carbon atoms provided that at least one of R1 and R2 represents the substituted or unsubstituted monovalent aliphatic hydrocarbon group having 1 to 20 carbon atoms or the substituted or unsubstituted aralkyl group having 7 to 20 carbon atoms; or R1 and R2 taken together represent a part of a ring structure having 3 to 20 ring atoms together with the carbon atom to which R1 and R2 bond.

Abstract: A resist underlayer film-forming composition includes a solvent, and a compound comprising an aromatic ring. The solvent includes a first solvent having a normal boiling point of less than 156° C., and a second solvent having a normal boiling point of no less than 156° C. and less than 300° C. The resist underlayer film-forming composition is for use in forming a resist underlayer film to be overlaid on a patterned substrate. A production method of a patterned substrate includes applying the resist underlayer film-forming composition on a patterned substrate to obtain a coating film on the patterned substrate. The coating film is heated to obtain a resist underlayer film. A resist pattern is formed on an upper face side of the resist underlayer film. The resist underlayer film and the substrate are etched using the resist pattern as a mask.

Abstract: A composition for resist underlayer film formation contains a compound having a group represented by formula (1), and a solvent. R1 represents an organic group having 2 to 10 carbon atoms and having a valency of (m+n), wherein the carbon atoms include two carbon atoms that are adjacent to each other, with a hydroxy group or an alkoxy group bonding to one of the two carbon atoms, and with a hydrogen atom bonding to another of the two carbon atoms; L1 represents an ethynediyl group or a substituted or unsubstituted ethenediyl group; R2 represents a hydrogen atom or a monovalent organic group having 1 to 20 carbon atoms; n is an integer of 1 to 3; * denotes a bonding site to a moiety other than the group represented by the formula (1) in the compound; and m is an integer of 1 to 3.

Abstract: The composition for film formation includes a compound including a group of the formula (1) and a solvent. In the formula (1), R1 to R4 each independently represent a hydrogen atom, a monovalent organic group having 1 to 20 carbon atoms, or R1 to R4 taken together represent a cyclic structure having 3 to 20 ring atoms together with the carbon atom or a carbon chain to which R1 to R4 bond. Ar1 represents a group obtained by removing (n+3) hydrogen atoms from an aromatic ring of an arene having 6 to 20 carbon atoms. n is an integer of 0 to 9. R5 represents a hydroxy group, a halogen atom, a nitro group, or a monovalent organic group having 1 to 20 carbon atoms.

Abstract: A composition for resist underlayer film formation, includes a first compound and a solvent. The first compound includes a first group represented by formula (1) and a partial structure comprising an aromatic ring. In the formula (1), R1 represents a single bond or an oxygen atom, R2 represents a divalent chain or alicyclic hydrocarbon group having 1 to 30 carbon atoms, and * denotes a bonding site to a moiety other than the first group of the first compound.

Abstract: A composition comprises a compound comprising a partial structure represented by formula (1) and comprising an intermolecular bond-forming group; and a solvent. X1 and X2 each independently represent a substituted or unsubstituted ring structure having 4 to 10 ring atoms constituted taken together with a spiro carbon atom and carbon atoms of an aromatic ring. R1 and R2 each independently represent a halogen atom, a hydroxy group, a nitro group or a monovalent organic group. a1 and a2 are each independently an integer of 0 to 8. n1 and n2 are each independently an integer of 0 to 2; k1 and k2 are each independently an integer of 0 to 8. A sum of k1 and k2 is no less than 1, and a sum of a1 and k1. A sum of a2 and k2 are no greater than 8.

Abstract: A method comprises applying a composition on a substrate to form a coating film on the substrate. The coating film is heated in an atmosphere in which an oxygen concentration is less than 1% by volume and a temperature is higher than 450° C. and 800° C. or lower, to form a film on the substrate. The composition comprises a compound comprising an aromatic ring. The oxygen concentration in the atmosphere during the heating of the coating film is preferably no greater than 0.1% by volume. The temperature in the atmosphere during the heating of the coating film is preferably 500° C. or higher and 600° C. or lower.

Abstract: A composition comprises a compound comprising a partial structure represented by formula (1) and comprising an intermolecular bond-forming group; and a solvent. X1 and X2 each independently represent a substituted or unsubstituted ring structure having 4 to 10 ring atoms constituted taken together with a spiro carbon atom and carbon atoms of an aromatic ring. R1 and R2 each independently represent a halogen atom, a hydroxy group, a nitro group or a monovalent organic group. a1 and a2 are each independently an integer of 0 to 8. n1 and n2 are each independently an integer of 0 to 2; k1 and k2 are each independently an integer of 0 to 8. A sum of k1 and k2 is no less than 1, and a sum of a1 and k1. A sum of a2 and k2 are no greater than 8.

Abstract: A resist underlayer film-forming composition includes a solvent, and a compound comprising an aromatic ring. The solvent includes a first solvent having a normal boiling point of less than 156° C., and a second solvent having a normal boiling point of no less than 156° C. and less than 300° C. The resist underlayer film-forming composition is for use in forming a resist underlayer film to be overlaid on a patterned substrate. A production method of a patterned substrate includes applying the resist underlayer film-forming composition on a patterned substrate to obtain a coating film on the patterned substrate. The coating film is heated to obtain a resist underlayer film. A resist pattern is formed on an upper face side of the resist underlayer film. The resist underlayer film and the substrate are etched using the resist pattern as a mask.

Abstract: A composition comprises a compound comprising a partial structure represented by formula (1) and comprising an intermolecular bond-forming group; and a solvent. X1 and X2 each independently represent a substituted or unsubstituted ring structure having 4 to 10 ring atoms constituted taken together with a spiro carbon atom and carbon atoms of an aromatic ring. R1 and R2 each independently represent a halogen atom, a hydroxy group, a nitro group or a monovalent organic group. a1 and a2 are each independently an integer of 0 to 8. n1 and n2 are each independently an integer of 0 to 2; k1 and k2 are each independently an integer of 0 to 8. A sum of k1 and k2 is no less than 1, and a sum of a1 and k1. A sum of a2 and k2 are no greater than 8.

Abstract: A composition comprises a compound and a solvent. The compound comprises a carbon-carbon triple bond-containing group, and at least one partial structure having an aromatic ring. A total number of benzene nuclei constituting the aromatic ring in the at least one partial structure is no less than 4. The at least one partial structure preferably comprises a partial structure represented by formula (1). The sum of p1, p2, p3 and p4 is preferably no less than 1. At least one of R1 to R4 preferably represents a monovalent carbon-carbon triple bond-containing group. The at least one partial structure also preferably comprises a partial structure represented by formula (2). The sum of q1, q2, q3 and q4 is preferably no less than 1. At least one of R5 to R8 preferably represents a monovalent carbon-carbon triple bond-containing group.

Abstract: A composition comprises: a compound having one partial structure represented by formula (1), and a solvent. n1 and n2 are each independently an integer of 0 to 2; and k1 and k2 are each independently an integer of 0 to 9. The compound preferably has an intermolecular bond-forming group. The compound is preferably represented by formula (2). Z represents the partial structure represented by the formula (1); Ar1 and Ar2 represent a substituted or unsubstituted arenediyl group having 6 to 20 carbon atoms; Ar3 and Ar4 represent a substituted or unsubstituted aryl group having 6 to 20 carbon atoms; and p1 and p2 are each independently an integer of 0 to 3.